Bizarrely enough, the one attempted comment I made at Yglesias that I bothered to copy before posting actually got through anyway. You can find the comment here, but I’ll reproduce it below.
“I just read Kuhn’s book and his account sounds different from yours. It did mention neo-Platonism, but I don’t recall it saying Copernicus was a member of any cult as a young man. Copernicus did not set out to abolish epicycles, he had to include a lot of them to make the predictions of his model fit the data. And the problem with his theory wasn’t just that orbits are ellipses rather than perfect circles like he assumed, it was also the case that a lot of the old data he was relying on was inaccurate and we needed new and better data from Tycho Brahe (still a Ptolemaist who had the sun go around the earth while most planets went around the sun) to get an accurate picture.”
To elaborate on what I wrote above, the innovation produced by Ptolemy that Copernicus really rejected was the equant. He rejected it because he (incorrectly) insisted on uniform circular motion and the way he replaced it was with epicycles, which Yglesias incorrectly states that Copernicus abolished! He seems to be repeating the myths that Kuhn set out to debunk. Kuhn also noted that Copernicus’ epicycles were of the “minor” variety, but I think that distinction may post-date the heliocentric model.

UPDATE 06/23/2018: The above link to Yglesias doesn’t work. His post is now here, with no comments.