There is a lot to respond to here. I'll start with this:
1) There are some significant reasons to conclude that the first Gospel was produced after Bar Kokhba.
2) My position is that the Marcionite version of the Pauline letters should be taken as the more authentic version of the letters, which is closer to their original form.
Firstly, other than a very few passages in the Pauline letters that indirectly indicate Jesus was a "messiah", which are also not in the Marcionite letters, there is no real theology developed around the concept of Jesus as a Messiah in the Pauline letters. We find the term "Christ" all over the Pauline letters, but as has long been acknowledged the term is used in the Pauline letters like a name in a way unfamiliar to other Jewish writings and of course in reality what we have is the nomina sacrum ΧΣ, which could mean "Christ" or "Chrest" (Good).
So there is certainly no strong or definitive indication that the Pauline letters identify Jesus as a "messiah" figure. Yet the Gospels clearly indicate that Jesus was at least some type of messiah. He is presented, rightly or wrongly, as the "King of the Jews".
Furthermore, the Gospel of Mark treats the messianic identity of Jesus as a "secret" that most people failed to recognize. This is a type of literary trope used to retroactively introduce new claims into the past. This indicates that the messianic identity of Jesus was a new concept being introduced by the first Gospel writer.
Here are a few scriptures that I believe are best explained as relating to Bar Kokhba:
Mark 13:
14 “But when you see the abomination of desolation standing where it should not be (let the reader understand), then those who are in Judea must flee to the mountains. 15 The one who is on the housetop must not go down, or go in to get anything out of his house; 16 and the one who is in the field must not turn back to get his coat. 17 But woe to those who are pregnant and to those who are nursing babies in those days! 18 But pray that it may not happen in the winter. 19 For those days will be a time of tribulation such as has not occurred since the beginning of the creation which God created until now, and never will.
We know that Hadrian erected a temple of Jupiter on the temple mount just prior to the Bar Kokhba revolt, and that Hadrian enacted harsh repressions against the Jews.
Mark 13:
21 And then if anyone says to you, ‘Behold, here is the Messiah’; or, ‘Behold, He is there’; do not believe him; 22 for false Messiahs and false prophets will arise, and will show signs and wonders, in order to lead astray, if possible, the elect. 23 But take heed; behold, I have told you everything in advance.
We know that Bar Kokhba was identified as the Messiah, and after the failure of his campaign he was maligned as a false messiah. He was also said to do signs and wonders.
Mark 15:
29 Those passing by were hurling abuse at Him, wagging their heads, and saying, “Ha! You who are going to destroy the temple and rebuild it in three days, 30 save Yourself, and come down from the cross!”
Why the talk of rebuilding? Bar Kokhba reportedly rebuilt a small temple on the temple mount and claimed to have liberate the temple. So here again we have a counter claim to Bar Kokhba. In this case, the writer is referring to a theological claim that Jesus himself is the temple, not a physical structure.
2 Thess 2:
2 Now we request you, brethren, with regard to the coming of our Lord Jesus Christ and our gathering together to Him, 2 that you not be quickly shaken from your composure or be disturbed either by a spirit or a message or a letter as if from us, to the effect that the day of the Lord has come. 3 Let no one in any way deceive you, for it will not come unless the apostasy comes first, and the man of lawlessness is revealed, the son of destruction, 4 who opposes and exalts himself above every so-called god or object of worship, so that he takes his seat in the temple of God, displaying himself as being God. 5 Do you not remember that while I was still with you, I was telling you these things? 6 And you know what restrains him now, so that in his time he will be revealed. 7 For the mystery of lawlessness is already at work; only he who now restrains will do so until he is taken out of the way. 8 Then that lawless one will be revealed whom the Lord will slay with the breath of His mouth and bring to an end by the appearance of His coming; 9 that is, the one whose coming is in accord with the activity of Satan, with all power and signs and false wonders, 10 and with all the deception of wickedness for those who perish, because they did not receive the love of the truth so as to be saved. 11 For this reason God will send upon them a deluding influence so that they will believe what is false, 12 in order that they all may be judged who did not believe the truth, but took pleasure in wickedness.
Neil reviews some of Turmel's case for the man of lawlessness/sin being Bar Kokhba:
https://vridar.org/2011/05/31/identifyi ... salonians/
There are essentially three main figures this passage seems likely to be referring to: Caligula, Hadrian, or Bar Kokhba. Two of these are from the same time period in the second century. Caligula never actually presented himself in the Temple, while apparently both Hadrian and Bar Kokhba at least in some fashion.
So here we have three passages in the scriptures that make a lot of sense in the context of the Bar Kokhba revolt.
2 Thess is often considered a pseudo-Pauline letter. So even if other Pauline letters were written in the first century, it is possible that 2 Thess was written in the 2nd century and that in fact the writing of 2 Thess may be related to the production of the Pauline letter collection. It may well be that the Pauline collection was assembled by the writer of 2 Thess or was prompted by the writing of 2 Thess. So several letters could have existed for some time, but it was the events of the Bar Kokhba revolt that led to the compilation of the collection in the early 130s. The writing of the first Gospel would have then soon followed.
The Pauline letters are clearly most occupied with the concept of Jesus as a figure who liberates mankind from the yoke of the law, who provides hope for resurrection of the dead and eternal life. Paul is concerned about morality and salvation from corruption, sin, injustice and earthly desires. The main writings of Paul are not concerned with conflict or larger political events, such as wars or major social upheavals.
Yet the first Gospel is very concerned about these things. The first Gospel is heavily pre-occupied with significant political events, with the destruction of the temple and the collapse of Judaism.
Why does the first Gospel present Jesus as a messiah who was unrecognized in his own time? A significant reason to do this would be to introduce the claim that it was not Bar Kokhba who was the Messiah, rather it was Jesus. The idea that Jesus was the Messiah doesn't come out of nowhere, it is a response to events that are related to the destruction of the Temple.
Mark appears to indicate that the movement of Bar Kokhba was misguided. Jesus was the messiah, but a different kind of messiah. Jesus rebuilt the temple, but a different kind of temple. Jesus is being touted as an answer to the failures of Bar Kokhba.
Is it possible that the first Gospel was written prior to the Bar Kokhba revolt and that the writer was motivated purely by events following the First Jewish-Roman War? Yes it is. But, the Bar Kokhba revolt provides better context for several specific aspects of the first Gospel. Yes, the setting of the crucifixion of Jesus under Pilate is closer to the First Jewish-Roman War, but this is far from definitive. In the case of the story of Elijah and Elisha, the ministries of Elijah and Elisha are set before the fall of the Northern Kingdom, but the story is clearly written after the subsequent fall of the Southern Kingdom. Nevertheless the ministries of Elijah and Elisha, set long before the later fall of the Southern Kingdom, are used to set the stage for the ultimate demise of the Southern Kingdom to the Babylonians and their destruction of the "First Temple".
Similarly, the first Gospel writer seems to view the First and Second/Third Jewish-Roman wars in a similar way as the two destruction events of Kings, where first the Northern Kingdom falls and then the Southern in two different conflicts. In this case, the two different conflicts happen to have taken place in the same region.