Eden,
I agree that Paul invented Christianity. He said he owed nothing to the Jerusalem Church. His writings were first and the others copied ideas from him, such as Jesus' words at the institution of the eucharist; he was not there and neither was any of the Gospel writers.
However, I think that the Jerusalem Church is represented in the NT Canon by Mark (follower of Peter) and by Matthew (given its Jewish focus, character and culture). The Matthew Gospel does give priority to Peter (as against Paul) as having the "keys to the kingdom".
As an aside, it is interesting to see how much use the NT writers made of the Jewish writings that are now considered apocryphal. And 2 Peter, which was written by a Pauline about 150 CE, is a commentary on Jude, which you say is Jewish Christian.
Doug