If they had resisted firmly, and Paul and the Apostles had been unable to rectify the situation, it would have demonstrated that the Holy Spirit was not with them, and that apostolic Christianity was false.
We seem to be talking past each other. You keep focusing on the outcome--whether they're listening to and obeying the Spirit--while I'm asking what Paul should have done. You refer to my question tangentially by saying "if Paul and the Apostles had been unable to rectify the situation." My question is, how should they have attempted to do so? It does no good to throw in that albatross about apostolic Christianity's falsity--we've already seen
correctible apostolic error when Paul confronted Peter.
Should Paul have argued? Would a point come when he must depart while God works on them?