So let's look at the evidence again. In our standard texts of Mark we have the following narrative preserved:
32 They were on their way up to Jerusalem, with Jesus leading the way, and the disciples were astonished, while those who followed were afraid. Again he took the Twelve aside and told them what was going to happen to him. 33 “We are going up to Jerusalem,” he said, “and the Son of Man will be delivered over to the chief priests and the teachers of the law. They will condemn him to death and will hand him over to the Gentiles, 34 who will mock him and spit on him, flog him and kill him. Three days later he will rise.”
35 Then James and John, the sons of Zebedee, came to him. “Teacher,” they said, “we want you to do for us whatever we ask.” 36 “What do you want me to do for you?” he asked. 37 They replied, “Let one of us sit at your right and the other at your left in your glory.” 38 “You don’t know what you are asking,” Jesus said. “Can you drink the cup I drink or be baptized with the baptism I am baptized with?” 39 “We can,” they answered. Jesus said to them, “You will drink the cup I drink and be baptized with the baptism I am baptized with, 40 but to sit at my right or left is not for me to grant. These places belong to those for whom they have been prepared.”
As we all know 'Secret Mark' places a hitherto unknown ritual - widely acknowledged to be a baptism rite - between the two paragraphs. Clearly if that rite was once there, it explains why the 'baptism' discussion that follows is raised. As it stands, one can just as well connect martyrdom with 'baptism' (as Origen says was common in his day) based on the structure of canonical Mark.
What is odd however - as Abbott notes - is that Matthew takes Mark's story and removes the baptism reference from it:
Now Jesus was going up to Jerusalem. On the way, he took the Twelve aside and said to them, 18 “We are going up to Jerusalem, and the Son of Man will be delivered over to the chief priests and the teachers of the law. They will condemn him to death 19 and will hand him over to the Gentiles to be mocked and flogged and crucified. On the third day he will be raised to life!”
20 Then the mother of Zebedee’s sons came to Jesus with her sons and, kneeling down, asked a favor of him. 21 “What is it you want?” he asked. She said, “Grant that one of these two sons of mine may sit at your right and the other at your left in your kingdom.” 22 “You don’t know what you are asking,” Jesus said to them. “Can you drink the cup I am going to drink?” “We can,” they answered. 23 Jesus said to them, “You will indeed drink from my cup, but to sit at my right or left is not for me to grant. These places belong to those for whom they have been prepared by my Father.”
In my mind the removal of the baptism reference and the emphasis on martyrdom derives from Matthew's reconstruction. We can see this a generation earlier where Irenaeus uses Matthew to help promote the idea that this story is about Jesus encouraging martyrdom:
"Then  drew near unto Him the mother of Zebedee's children, with her sons, worshipping, and seeking a certain thing from Him."  These people are certainly not void of understanding, nor are the words set forth in that passage of no signification: being stated beforehand like a preface, they have some agreement with those points formerly expounded.
"Then drew near." Sometimes virtue excites our admiration, not merely on account of the display which is given of it, but also of the occasion when it was manifested. I may refer, for example, to the premature fruit of the grape, or of the fig, or to any fruit whatsoever, from which, during its process [of growth], no man expects maturity or full development; yet, although any one may perceive that it is still somewhat imperfect, he does not for that reason despise as useless the immature grape when plucked, but he gathers it with pleasure as appearing early in the season; nor does he consider whether the grape is possessed of perfect sweetness; nay, he at once experiences satisfaction from the thought that this one has appeared before the rest. Just in the same way does God also, when He perceives the faithful possessing wisdom though still imperfect, and but a small degree of faith, overlook their defect in this respect, and therefore does not reject them; nay, but on the contrary, He kindly welcomes and accepts them as premature fruits, and honours the mind, whatsoever it may be, which is stamped with virtue, although not yet perfect. He makes allowance for it, as being among the harbingers of the vintage,  and esteems it highly, inasmuch as, being of a readier disposition than the rest, it has forestalled, as it were, the blessing to itself.
Abraham therefore, Isaac, and Jacob, our fathers, are to be esteemed before all, since they did indeed afford us such early examples of virtue. How many martyrs can be compared to Daniel? How many martyrs, I ask, can rival the three youths in Babylon, although the memory of the former has not been brought before us so conspicuously as that of the latter? These were truly first-fruits, and indications of the [succeeding] fructification. Hence God has directed their life to be recorded, as a model for those who should come after.
And that their virtue was thus accepted by God, as the first-fruits of the produce, hear what He has Himself declared: "As a grape," He says, "I have found Israel in the wilderness, and as first-ripe figs your fathers."  Call not therefore the faith of Abraham merely blessed because he believed. Do you wish to look upon Abraham with admiration? Then behold how that one man alone professed piety when in the world six hundred had been contaminated with error. Dost thou wish Daniel to carry thee away to amazement? Behold that [city] Babylon, haughty in the flower and pride of impiousness, and its inhabitants completely given over to sin of every description. But he, emerging from the depth, spat out the brine of sins, and rejoiced to plunge into the sweet waters of piety. And now, in like manner, with regard to that mother of Zebedee's children, do not admire merely what she said, but also the time at which she uttered these words. For when was it that she drew near to the Redeemer? Not after the resurrection, nor after the preaching of His name, nor after the establishment of His kingdom; but it was when the Lord said, "Behold, we go up to Jerusalem, and the Son of man shall be delivered to the chief priests and the scribes; and they shall kill Him, and on the third day He shall rise again." 
These things the Saviour told in reference to His sufferings and cross; to these persons He predicted His passion. Nor did He conceal the fact that it should be of a most ignominious kind, at the hands of the chief priests. This woman, however, had attached another meaning to the dispensation of His sufferings. The Saviour was foretelling death; and she asked for the glory of immortality. The Lord was asserting that He must stand arraigned before impious judges; but she, taking no note of that judgment, requested as of the judge: "Grant," she said, "that these my two sons may sit, one on the right hand, and the other on the left, in Thy glory." In the one case the passion is referred to, in the other the kingdom is understood. The Saviour was speaking of the cross, while she had in view the glory which admits no suffering. This woman, therefore, as I have already said, is worthy of our admiration, not merely for what she sought, but also for the occasion of her making the request.
She did indeed suffer, not merely as a pious person, but also as a woman. For, having been instructed by His words, she considered and believed that it would come to pass, that the kingdom of Christ should flourish in glory, and walk in its vastness throughout the world, and be increased by the preaching of piety. She understood, as was [in fact] the case, that He who appeared in a lowly guise had delivered and received every promise. I will inquire upon another occasion, when I come to treat upon this humility, whether the Lord rejected her petition concerning His kingdom. But she thought that the same confidence would not be possessed by her, when, at the appearance of the angels, He should be ministered to by the angels, and receive service from the entire heavenly host. Taking the Saviour, therefore, apart in a retired place, she earnestly desired of Him those things which transcend every human nature.
Clearly then Matthew leads one to understand martyrdom to be the 'baptism' referenced in Mark and it accomplishes this by negating the reference to 'baptism' altogether. How convenient! But we should never lose sight of the fact that 'baptism' was originally referenced in this narrative. What Matthew does is prevents us from seeing it wholesale.
Moreover Mark as it now stands in our canon makes explicit reference to baptism only in Mark 10:35. Only Secret Mark has the actual baptism (or at least hints at its existence). Those however who understand this section to be about a 'secret baptism' - even a heavenly ascent are heretics, heretics whom Irenaeus identifies as 'those of Mark':
It happens that their tradition respecting redemption(10) is invisible and incomprehensible, as being the mother of things which are incomprehensible and invisible; and on this account, since it is fluctuating, it is impossible simply and all at once to make known its nature, for every one of them hands it down just as his own inclination prompts. Thus there are as many schemes of "redemption" as there are teachers of these mystical opinions. And when we come to refute them, we shall show in its fitting-place, that this class of men have been instigated by Satan to a denial of that baptism which is regeneration to God, and thus to a renunciation of the whole [Christian] faith.
2. They maintain that those who have attained to perfect knowledge must of necessity be regenerated into that power which is above all. For it is otherwise impossible to find admittance within the Pleroma, since this [regeneration] it is which leads them down into the depths of Bythus. For the baptism instituted by the visible Jesus was for the remission of sins, but the redemption brought in by that Christ who descended upon Him, was for perfection; and they allege that the former is animal, but the latter spiritual. And the baptism of John was proclaimed with a view to repentance, but the redemption by Jesus(11) was brought in for the sake of perfection. And to this He refers when He says, "And I have another baptism to be baptized with, and I hasten eagerly towards it."(12) Moreover, they affirm that the Lord added this redemption to the sons of Zebedee, when their mother asked that they might sit, the one on His right hand, and the other on His left, in His kingdom, saying, "Can ye be baptized with the baptism which I shall be baptized with?"(13) Paul, too, they declare, has often set forth, in express terms, the redemption which is in Christ Jesus; and this was the same which is handed down by them in so varied and discordant forms.
3. For some of them prepare a nuptial couch, and perform a sort of mystic rite (pronouncing certain expressions) with those who are being initiated, and affirm that it is a spiritual marriage which is celebrated by them, after the likeness of the conjunctions above. Others, again, lead them to a place where water is, and baptize them, with the utterance of these words, "Into the name of the unknown Father of the universe--into truth, the mother of all things--into Him who descended on Jesus--into union, and redemption, and communion with the powers." Others still repeat certain Hebrew words, in order the more thoroughly to bewilder those who are being initiated, as follows: "Basema, Chamosse, Baoenaora, Mistadia, Ruada, Kousta, Babaphor, Kalachthei."(1) The interpretation of these terms runs thus: "I invoke that which is above every power of the Father, which is called light, and good Spirit, and life, because Thou hast reigned in the body." Others, again, set forth the redemption thus: The name which is hidden from every deity, and dominion, and truth which Jesus of Nazareth was clothed with in the lives(2) of the light of Christ--of Christ, who lives by the Holy Ghost, for the angelic redemption. The name of restitution stands thus: Messia, Uphareg, Namempsoeman, Chaldoeaur, Mosomedoea, Acphranoe, Psaua, Jesus Nazaria.(3) The interpretation of these words is as follows: "I do not divide the Spirit of Christ, neither the heart nor the supercelestial power which is merciful; may I enjoy Thy name, O Saviour of truth!" Such are words of the initiators; but he who is initiated, replies, "I am established, and I am redeemed; I redeem my soul from this age (world), and from all things connected with it in the name of Iao, who redeemed his own soul into redemption in Christ who liveth." Then the bystanders add these words, "Peace be to all on whom this name rests." After this they anoint the initiated person with balsam; for they assert that this unguent is a type of that sweet odour which is above all things.
4. But there are some of them who assert that it is superfluous to bring persons to the water, but mixing oil and water together, they place this mixture on the heads of those who are to be initiated, with the use of some such expressions as we have already mentioned. And this they maintain to be the redemption. They, too, are accustomed to anoint with balsam. Others, however, reject all these practices, and maintain that the mystery of the unspeakable and invisible power ought not to be performed by visible and corruptible creatures, nor should that of those [beings] who are inconceivable, and incorporeal, and beyond the reach of sense, [be performed] by such as are the objects of sense, and possessed of a body. These hold that the knowledge of the unspeakable Greatness is itself perfect redemption. For since both defect and passion flowed from ignorance, the whole substance of what was thus formed is destroyed by knowledge; and therefore knowledge is the redemption of the inner man. This, however, is not of a corporeal nature, for the body is corruptible; nor is it animal, since the animal soul is the fruit of a defect, and is, as it were, the abode of the spirit. The redemption must therefore be of a spiritual nature; for they affirm that the inner and spiritual man is redeemed by means of knowledge, and that they, having acquired the knowledge of all things, stand thenceforth in need of nothing else. This, then, is the true redemption.
5. Others still there are who continue to redeem persons even up to the moment of death, by placing on their heads oil and water, or the pre-mentioned ointment with water, using at the same time the above-named invocations, that the persons referred to may become incapable of being seized or seen by the principalities and powers, and that their inner man may ascend on high in an invisible manner, as if their body were left among created things in this world, while their soul is sent forward to the Demiurge. And they instruct them, on their reaching the principalities and powers, to make use of these words: "I am a son from the Father--the Father who had a pre-existence, and a son in Him who is pre-existent. I have come to behold all things, both those which belong to myself and others, although, strictly speaking, they do not belong to others, but to Achamoth, who is female in nature, and made these things for herself. For I derive being from Him who is pre-existent, and I come again to my own place whence I went forth." And they affirm that, by saying these things, he escapes from the powers. He then advances to the companions of the Demiurge, and thus addresses them:--"I am a vessel more precious than the female who formed you. If your mother is ignorant of her own descent, I know myself, and am aware whence I am, and I call upon the incorruptible Sophia, who is in the Father, and is the mother of your mother, who has no father, nor any male consort; but a female springing from a female formed you, while ignorant of her own mother, and imagining that she alone existed; but I call upon her mother." And they declare, that when the companions of the Demiurge hear these words, they are greatly agitated, and upbraid their origin and the race of their mother. But he goes into his own place, having thrown [off] his chain, that is, his animal nature. These, then, are the particulars which have reached us respecting "redemption."(1) But since they differ so widely among themselves both as respects doctrine and tradition, and since those of them who are recognised as being most modern make it their effort daily to invent some new opinion, and to bring out what no one ever before thought of, it is a difficult matter to describe all their opinions.
Pretty convincing evidence IMHO that from ''Secret Mark' to canonical Mark to Matthew there is a systematic 'reworking' of the original meaning of the section - i.e. what it is all about.
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote