Peter ADDRESSED the council, he did not oversee it. If there was a common understanding that HE was the leader of the new church and infallible, no one would have questioned him, and certainly he would have been the one in charge of the 1st church council.
In fact, your own timeline shows St,. Peter in "Babylon" in AD 66, full 15 years later. That Babylon was code word for Rome, not the ruins of Babylon in Mesopothamia, which no one had any business visiting
Now if as Protestant says Babylon the great in Revelations there is a huge outcry, are you saying that Babylon in scripture IS Rome?
Eusebius relates that by Babylon Peter meant Rome " but that cannot be proved, nor is there any reason be given why the proper name of the place should be concealed, and a figurative one expressed.
Babylon in Assyria,was the metropolis of the dispersion of the Jews . Peter was the apostle to the circumcision, so it would seem in obedience to God that is where he should have been. This area of the world contained may of the "purest Jews" . It was a place of learning with Universities there .
There is nothing to indicate that Peter was in Rome when Paul wrote that letter. He certainly would not have left the name of the POPE out of his greeting. He certainly would not have planed to catechize the church in Rome if peter had been there.
While it is true that the epistles were circulated throughout the church, the ones to whom it was first sent is clearly stated under the operation of the Holy Spirit. All the disciples preached to whomever had ears, but God had divided the work of the church and there is no indication that it was ever changed.
Paul felt called to go to Rome because his call was to the Gentiles. (The Jews had been sent out of Rome)
There is no evidence that Peter was ever in Rome except folk lore that has never been proved historically, as there is no contemporary work to verify that.
It is true that St. Peter did not preside over that council. No one claims he was Pope at that time. No one claims that the word "Pope" was in use that early either. Popes today also face significant opposition and promulgate their agenda often with great difficulty. It is in fact remarkable that a vision from God alone was sufficient for the Jerusalem council to abandon the centerpiece of Mosaic law, the dietetic rules. If St. Peter was not recognized as one with the special commission from Christ, he would not have been able to stand Mosaic Law on its head just because he had a dream. But pope he was not, at the time.
Babylon has always been a metaphore for temporal evil. Surely historical scripture refers to the actual Babylon, but it does not prevent St. Peter to refer to Rome, the center of evil temporal power of his day. It is certainly reasonable that he would use a code word to describe his whereabouts in times of persecution.
There is a firm record of St. Mark, St. Peter's secretary, martyred in Rome.
Whether any of that amounts to solid historical proof, matters little. We don't have a solid historical proof of many events we nevertheless know from the Holy Tradition. If you refuse to listen, that is your loss.