Paul met with the other Apostles and probably avoided a church split. The compelling evidence was the gentiles were filled by the spirit just as the Jew's were. Miracles among the gentiles convinced everyone that the grace of Christ was all that was necessary to be saved (Acts 15)
The most compelling argument I can give to my fundi brothers and sisters that we have received the same grace (GLBT vs. heterosexual) is that we walk in the same light.
Paul told stories of how God had done great things among the gentiles.
What great things have you seen God do in you life that would show God moves in your life just like he seems to in the lives some good old Southern Baptist or some more Pentecostal groups? What has Jesus done for you?