And here's another point. His claims notwithstanding, so far as I know the Catholic Church has never claimed a flat Earth. Geocentrism, yes. Flat Earth, no. So even denying Vatican II does him no good; he's claiming their support for something that was never doctrine in the nearly two thousand years of the existence of Christianity. Come to that, even though the apology to Galileo was from John Paul II, the Church had been accepting of heliocentrism for some time before that. I'd have to go back and look it up, but probably within a hundred years of Galileo's death. By which point it had become clear that continuing to deny it made them look foolish, though not anywhere near so foolish as claiming a flat Earth would.