"But this passage is more about division of labor rather than the legitimacy of preaching to the Gentiles."
------ Wouldn't one labor where one's calling and authority was? Wasn't Paul specifically chosen by the Resurrected Jesus to take the Gospel to the Gentiles? He had a mission specifically given to him by the Resurrected Jesus to go to the Gentiles. Peter did not. He labored where his authority was --- among the Jews.
After being personally converted by Jesus Saul/Paul was sent to the nascent Catholioc Church to have his blindness cured and to get a quick catechesis.