Christians, would you have saved Jesus, if you had he chance?

[Angrboda]

...Anachronisms in the text of the old testament point to it having been largely composed in the 6th and 7th centuries BCE, despite appearing to narrate older events. [1] The older events need not have become legend and stories at the time specified in the later codification of them, just as the beginning of the legends about Jesus need not have occurred in 33 CE.  If the legends about Jesus had their beginnings several decades earlier, that gives plenty of time for a church to develop around the legends. [2] The dates of the birth and crucifixion would have been back filled later, decades after the supposed events. [3]

1) True. It is also apparent that those texts, as we have them today, are largely the result of multiple redactions and combinations of smaller, older texts into a whole (e.g. The single unity of the ancient Throne-Succession Narrative split and redacted into 2 Sam 9-20 and 1 Kgs 1-2). So while it is true that the texts began to be compiled into a unity in the 6th and 7th century BCE, the compiled texts (e.g. the succession narrative) have been found to precede the redaction by centuries.

The point however is that these redacted texts need not represent the actual chronology of the events they describe as they weren't necessarily written contemporaneous with the events they describe.

2) True. And you might expect to find evidence of such legends dating from those decades. As far as I know, there is no such evidence, and the only non-Christian attestation of any sort of Jesus character comes decades afterward, not before. 

If the Pauline epistles are any indication, letters were being written between the various churches by approximately 50 CE. That we don't have evidence of these other letters makes your expectation an unrealistic one. Also, much of the so to speak expected documents would not exist as the tradition may have been largely oral.

Also, Justin Martyr (100-165 AD), when writing to the Emperor about the Christian religion, assures the Emperor that he can verify that a Jesus of Nazareth was crucified under pilate in a document called "The Acts of Pilate" (which is to be distinguished from the 4th century apocryphal texts). did such a document exist? That is unclear, but it is clear the Justin thought it was a simple enough claim to tell the Emperor "You can check Pilate's notes, all of it is in there".

What Justin Martyr may have thought during the second century is little evidence of what transpired a century earlier.

3) Maybe, but like the rest of the ancient world, authors measured time by who was in charge. In this case: Pontius Pilate and Tiberius in the case of the crucifixion. I also recognize the difficulties in dating the birth of Jesus. His crucifixion is much easier to date.

By what means are you dating the crucifixion? As pointed out, the Gospels come too late to bear indisputable evidence of when the 'events' in them actually occurred. They claim that they occurred under Pilate and Tiberius, but that could just be an arbitrarily asserted connection. As you said yourself, people at the time dated events by who was in charge; so if you wanted to place a narrative in a certain time, you would claim the participation of historic figures. That would explain why Pilate is involved in the sentencing of an obscure rabbi; simply put, he wasn't. Inserting Pilate into the story is just a false dating of events.