Why do you lay stress on Paul "converting" when people who are Jewish by ancestry didn't need to convert? (Becoming a Pharisee wasn't a conversion, it was essentially a handshake and a promise.)

Are you familiar with the many Pharisees who accepted Jesus as Messiah? Not just Paul, but probably Hillel, then Nicodemus, Joseph, the scribe not far from the kingdom, and Gamaliel are known, and there are indications of many others in the movement. The siege of Jerusalem (from which the Christians escaped) was the point from which Pharisaism consolidated without Jesus, before which it had remained an open question. And when it was open, some Pharisees supported and some rejected, just as you note. The exact circumstance is in Acts 8:1-3, where Saul has just officiated at Stephen's "execution" and zealously persecuted other Christians in Jerusalem with the support of those who had Stephen persecuted (this was about 36, with the stronger leadership of James coming quite later, more like 45). The other narratives of Acts 8 indicate results of the dispersion before focusing back on Saul's reaction to his Jerusalem work being so well-supported, namely his zeal to go to Damascus; that literary decision is justified because that trip led to a lot of consequence for the whole and needed to be dealt with fully and separately from the Acts 8 narratives. So I don't see anything problematic, and I do see a little bit of potential anachronism between Saul and James.

Anyway, I'm glad we're all crossing online tonight, I respect your opinion, which is why my other comment asks how you like to work together when we have divergent opinions.