No one has even attempted to prove the "traditions" are the same. They can't.
>>P.S.: Paul's statement was in the context of all the apostles in communion with Peter as Head of Christ's Church who could not err in teaching contrary to the Faith.<<
Paul specifically referenced the Gentiles making the statement "giving them the Holy Spirit, just as He also did to us; 9and He made no distinction between us and them,". That cannot possibly be used for what you would like.
It's curious. This insistence on sameness and continuity as a determiner of Truth. These are attributes of human analytical thought and according to the protestant have no bearing on the truth anywhere else in theology, except here. Of course it also depends on whether someone is referring to "traditions" in the pejorative sense or Tradition. Incidentally we Catholics refer to it as Sacred Tradition and not Traditions because Sacred Tradition has a singular quality to it signifying continuity. Which is what the protestant is apparently searching for.