As one can imagine, this lead them to find the errors in the old geocentric model pretty quickly.
This part of your description trips me up. It sounds like you have an established tradition of looking at the stars, so my question is: Why do the errors in the geocentric model become an issue at this point in time? Is it new advances in technology allowing more accurate measurements, or is it a changing political climate that allows people to voice their concerns more openly?
As for the magic, have you thought about your "message"? I think my main concern with including the magic is that you seem to be taking a scientific point of view, valuing reason over faith. If you include something supernatural, that could counter that somewhat.
On the other hand, including magic will remove it farther from being an analog of Renaissance Europe. You're already pretty far from that, of course. I think that having the main characters not possess magic in a world where magic exists is a bonus, though--just because almost every author succumbs to the idea that no one can be more special than their darling.