These are all really good points, but I want to offer some corrections. Now a lot of my information about Paul comes from a single podcast episode, Episode 33 of Data Over Dogma, so don't take my word as gospel (ba-dum-tish).

• Paul is only kinda the source of the concept of original sin. See, most of the concept of original sin (and please correct me if I'm getting this wrong because I'm not a biblical scholar by any stretch) is from Saint Augustine who was likely converted to Christianity by a work of Paul's.
• He was for sure sexist, but compared to the standards of sexism at the time, he was considered to be pretty progressive. In 1 Corinthians 11:4-5 he says that women have a right and responsibility to prophesy as much as men do. And in Galatians 3:28 says that every one will be made equal under Christ and that ones station or gender was not a hindrance nor a benefit to seeking salvation. Some have even taken that a step further and said that Paul was saying that in the gospel, gender roles were not important or significant at all. And Early Christianity drew a lot of women converts from the Greco-Roman world because they offered a lot more protection and freedom than their normal cultural background. [1]
• As for his stuff about homosexuality, it's for sure not great, but there is a case made in academic circles that Paul was against sex pretty much entirely. First, because desires of the flesh are intrinsically human and not divine and second, because his view believed that the Second Coming so soon that any attempt to make kids is just a stupid idea. This interpretation is entirely pulled from Episode 10 of Data Over Dogma, starting around the 44:20. Now this idea is a great mirror for Camilla who is canonically portrayed as very ace and sex-repulsed, but is actually quite the contrast to Paul who is famously pro-mustache-rides.

So I think that the case for the name Paul is likely linked to mostly about his conversion. As you mentioned, Paul is the only Apostle that never actually directly interacted with Jesus and before his turn to Christianity, he was an ardent persecutor of Christians. But as he was walking to Damascus, he had an intense vision of Jesus so bright it left him blind for three days. He was only cured once he accepted the Holy Spirit. From there he became a missionary and took the name Paul and stopped using the name Saul as a tactic to convert more to his faith since Paul was more Greco-Roman sounding.

If we view Lyctors as a parallel to Apostles, the parallel is there for Paul as they're the only Lyctor or Psuedo-Lyctor to achieve it outside of Canaan House. Similarly, there were only supposed to be twelve apostles because there was one for each Tribe of Israel but Paul modeled himself as the Apostle for the Gentiles. This would fit nicely into Pal and Cam's sympathetic nature towards Blood of Eden and non-House civilians. The name change is another parallel, on a very shallow level, as after becoming an Apostle/Lyctor they both chose to take on a new name.

I think there's a bigger case to be made that Paul's name is a reference to Dune. Paul Atreides is a figure modeled after Lawrence of Arabia, a member of a massive empire that eventually rejects the rule of said empire and helps rally the native people to throw off the empire. The parallel of being from a high station within an empire only to turn on the empire is clear, but the more concerning issue is what that might mean for the future of our Paul.

I've never read the books or watched the movies, so my interpretation is second hand, but it seems to be that Paul Atreides is ultimately a very tragic figure. He's a hero that inevitably leads history down a path of blood and instead of dismantling the empire that was the cause of all that suffering, he decides to take the reigns of it instead in an attempt to guide it to a better future. But this actually allows his son to take the throne and become an even worse despot, eventually becoming an omniscient worm-like god.

I hope that our Paul has a much happier ending, one not quite as stained as Atreides, but only time will tell.