Paul made it quite clear that Christians are to submit to the...

Paul made it quite clear that Christians are to submit to the governing authorities.

Did they disband their off-shoot cult back in Paul's day, and submit to the Jewish religious hierarchies ruling that the Messiah hadn't turned up yet?

I can't see any submission on the part of the Christian cult. The Jews and the Romans made it quite clear that they were a dangerous cult, yet they didn't drop their activity of continuing to harvest followers and promote the idea of Jesus as the Messiah.