And just to highlight where we agree and where we differ with Ken and where I likely go beyond you in terms of active speculation of the Alexandrian Markan tradition:
1. in the late third century there was a cult of St Mark as founder of the Alexandrian church located EXACTLY where later tradition says it began - i.e. the eastern shores of Alexandria in a region called 'the Cattle pasture.'
But they took him up and brought him to the place called Bucolia, where the holy St. Mark underwent martyrdom for Christ. Astonishing is the virtue of the saints! As they carried him along, and beheld his great constancy and strength of mind when in peril of death, on a sudden a fear and trembling came upon them to such a degree, that none of them could look steadfastly into his face. Moreover, the blessed martyr entreated them to allow him to go to the tomb of St. Mark, for be desired to commend himself to his patronage. But they from confusion, looking down on the ground, said, Do as you wish, but make haste. Therefore approaching the burial-place of the evangelist, he embraced it, and speaking to him as if he were yet alive in the flesh, and able to hear him, he prayed after this manner: O father most honourable, you evangelist of the only-begotten Saviour, you witness of His passion, you did Christ choose, who is the Deliverer of us all, to be the first pontiff and pillar of this See; to you did He commit the task of proclaiming the faith throughout the whole of Egypt and its boundaries. You, I say, hast watchfully fulfilled that ministry of our human salvation which was entrusted to you; as the reward of this labour you have doubtless obtained the martyr's palm. Hence, not without justice, are you counted worthy to be saluted evangelist and bishop. Your successor was Anianus, and the rest in descending series down to the most blessed Theonas, who disciplined my infancy, and deigned to educate my heart. To whom I, a sinner and unworthy, have been beyond my deservings appointed as successor by an hereditary descent. And, what is best of all, lo! The largeness of the divine bounty has granted me to become a martyr of His precious cross and joyful resurrection, giving to my devotion the sweet and pleasant odour of His passion, that I should be made meet to pour out unto Him the offering of my blood. And because the time of making this offering is now instant, pray for me that, the divine power assisting me, I may be meet to reach the goal of this agony with a stout heart and ready faith. I commend also to your glorious patronage the flock of Christ's worshippers which was committed to my pastoral care; to you, I say, I with prayers commend it, who are approved as the author and guardian of all preceding and subsequent occupiers of this pontifical chair, and who, holding its first honours, art the successor not of man, but of the God-man, Christ Jesus. Saying these words, he went back to a little distance from the sacred tomb, and, raising his hands to heaven, prayed with a loud voice, saying: O you Only-begotten, Jesus Christ, Word of the Eternal Father, hear me invoking Your clemency.Speak peace, I beseech You, to the tempest that shakes Your Church, and with the effusion of my blood, who am Your servant, make an end to the persecution of Your people. Then a certain virgin dedicated to God, who had her cell adjoining to the tomb of the evangelist, as she was spending the night in prayer, heard a voice from heaven, saying: Peter was the first of the apostles, Peter is the last of the martyred bishops of Alexandria.
Having ended his prayer, he kissed the tomb of the blessed evangelist, and of the other pontiffs who were buried there, and went forth to the tribunes. But they seeing his face as it had been the face of an angel, being terror-stricken, feared to speak to him of his instant agony. Nevertheless, because God does not desert those who trust in Him, He willed not to leave His martyr without consolation in the moment of so great a trial. For lo! An old man and an aged virgin, coming from the smaller towns, were hastening to the city, one of whom was carrying Four skins for sale, and the other two sheets of linen. The blessed prelate, when he perceived them, recognised a divine dispensation with reference to himself. He inquired of them on the instant, Are you Christians? And they replied, Yes. Then said he, Whither are you going? And they replied, To the market in the city to sell these things that we are carrying. Then the most merciful father answered, My faithful children, God has marked you out, persevere with me. And they immediately recognising him, said, Sire, let it be as you have commanded. Then turning to the tribunes, he said, Come, do what you are about to do, and fulfil the king's command; for the day is now on the point of breaking. But they, suffering violence as it were on account of the wicked decree of the prince, brought him to a spot opposite to the sanctuary of the evangelist, into a valley near the tombs. Then said the holy man, Spread out, you aged man, the skins which you carry; and you too, O aged woman, the linen sheets. And when they had been spread out, this most constant martyr, mounting upon them, extended both his hands to heaven, and bending his knees on the ground, and fixing his mind upon heaven, returned his thanks to the Almighty Judge of the contest, and fortifying himself with the sign of the cross, said, Amen. Then loosening his omophorion from his neck, he stretched it forth, saying, What is commanded you, do speedily.
Meanwhile the hands of the tribunes were paralyzed, and looking upon one another in turn, each urged his fellow to the deed, but they were all held fast with astonishment and fear. At length they agreed that out of their common stock a reward for the execution should be appointed, and that the man who should venture to perpetrate the murder should enjoy the reward. There was no delay, each of them brought forth five solidi. But, as says the heathen poet —
Quid non mortalia pectora cogis, Auri sacra lames? one of them, after the manner of the traitor Judas, emboldened by the desire of money, drew his sword and beheaded the pontiff, on the 25th day of November, after he had held the pontificate twelve years — three of which were before the persecution, but the nine remaining were passed by him under persecutions of diverse kinds.
2. Even if the Acts of Peter of Alexandria are dated in its final form to the fifth century it necessarily details foundational elements of the Alexandrian tradition which were established in the late third century - i.e. Boucalia (the old Jewish quarter of Alexandria becoming the center of Christianity).
3. These traditions are confirmed by Arius being the bishop or priest of the Church of St Mark in Alexandria and thus the de facto Pope of Egypt (even if that honorific title was not openly used by those associated with him).
4. Intimations of early Arians that previous generations of Popes held the same 'Arian' beliefs as him necessarily implies a Markan tradition which ascribed the Logos to be a 'creature' and to have not existed when only the Father existed. In other words, you can follow a chain of thought from Arius not only to Mark but Philo of Alexandria because the heretical Logos doctrine of the Arians was Markan and moreover ultimately Alexandrian Jewish.