Can you provide any Papal reference to the earth being flat? 
Well, there's the holy book of the Papacy, which in at least one verse claims that the entirety of the Earth is visible from the peak of the highest mountain. Not really possible with a geoid. There are also references to the four corners, although to the best of my knowledge they were intended as metaphorical. There is a reason many people believe TFES to be a group of biblical literalists.
I don't think that was what Manarq was referring to, however. Rather, the major change is that of geocentrism, with the Earth being the center of the solar system, to heliocentrism with the sun being the center of the solar system, based upon the same force that drives Earth into a rough sphere and some simpler mathematics.
To play to your side, Ski, by the time the Church formed, it was mostly common knowledge that the Earth was roughly spherical, thanks to the ancient philosophers and mathematicians. To continue playing to Manarq's, the Papal view of the Earth's position in the cosmos was changed radically by the same evidence that presents Earth as a geoid.