This is rather a silly argument. It is like saying that John was the only disciple that Jesus loved, just because that is how John recalls his Divine Master and his relationship to Him. I can’t imagine the other Twelve calling John by the title, the disciple that Jesus loved, especially given the sons’ of Zebedee proclivity to aspiring to be the best by having the best positions. This was John’s simple and humble way of referring to himself in answer to his own pride.
All the Apostles followed the same modus operandi. When they went to a new area, they first sought out the Jewish community and announced the Gospel as the fulfillment of the Covenant and the Prophecies, and they answered arguments with scriptural and theological reasoning. Then they moved on, just as Paul did. Paul recognized that he had been called to the Gentile churches and lands, originally by Barnabas, but then confirmed by Peter at Jerusalem. What he means by, Peter to the Jews and he to the Gentiles, is, a recognition of Peter’s role as head of the visible church. That is to say, the Apostles recognized that they had a problem, so to speak, in the transition from the Old Covenant to the New, and bringing as many of the Jews into the Church of the Messiah as possible. It was left to Peter, as head of the Church, to deal with that problem. Peter named James the Less, an Apostle, to head the Church of Jerusalem, and to limit his ministry to handling that problem, and he became such an edification to the Jews with his exemplary life, that they called him “the Just”. Peter was delayed in leaving Jerusalem by addressing this problem, and seeing that it was handled rightly. It was of the utmost importance that the theological explanations and proofs be provided for the transition in the most respectful way to do justice to the faith of the Patriarchs and Prophets. The rest of the Apostles, like James the Greater, left much earlier to different lands, to those with known Jewish settlements first. Paul was simply saying that Jerusalem was Peter’s problem, not his, in spite of his deeper education in Jewish Law and Scripture. His mission lay with fulfilling the prophecies about the opening of faith to the nations. As Paul was aware, the whole Church was an opening to the Gentile Nations, and all the Apostles were bringing true worship to heathens that had rejected it since Babel. He, as also the other Apostles, was painfully aware that the rejection of Christ by the Jewish leaders was an historic event that would mean that the Church would not be whole until much later in history when they would finally accept Christ and come into the Church. Paul knows the pain and the division of this, yet sees it as providential. Peter did not himself stay in Jerusalem, nor was it said that he was its first bishop, because he ultimately was the head of the Gentile Church, and had to set his see and headship at the center of the Gentile world, Rome.
Paul also saw the fulfillment of his ministry as giving witness to Rome, and long aspired to go there. His mission to Jerusalem was only to be charitable with funds to support the Church there under great pressure from the Jews, and to demonstrate that there was no division between himself and James. He had Rome as his objective, again with its large Jewish presence. But he said his work in Asia minor was complete, and he was looking for further lands to evangelize, not martyrdom per se. He was rejoicing that now the whole world would be submitting themselves to true worship of the True God through the enlightenment of Christ, our Savior. It was God who decided that He wanted both His witnesses to give their ultimate and lasting witness together there.