However, let's pretend that, for some reason, in modern society today, people still use the geocentric model, aka the earth is stationary and the sun and everything else revolves around the sun.
1) How far into bizarro land will I need to twist the Ptolemaic system to account for various things we know in astronomy (stars twinkling, Galileo's observations, Kepler's laws, etc.)
I really don't care how bizarro I'll need to get; I actually want to create this giant mess, that I can later refute. It may help that my fictional modern society has magic and gods, and Absolutely And Resolutely Believes that the gods raise the sun and moon (and yet for some reason still tries applying the laws of physics to everything else). Right now I'm using the excuse of said magical gods have created a magical veil around earth that allows them to affect how the sun's light and moon's appearance comes into view to an observer on earth, but everything else follows modern astronomy (including the actual fact that the earth revolves around the sun). Also, my fictional society has not gone space age yet and so we don't have to worry about things like the Hubble telescope and satellite information enlightening everyone yet.
2) Other than the brief examples I listed earlier, what are various proofs that shows that the earth revolves around the sun?
Copernicus, Galileo, Kepler (and Newton) are the big ones I know, and a few things like twinkling stars and parallax (which I only vaguely understand), but what other observational proofs are there that show that the geocentric model is really, really dumb? In other words, what holes will still exist in my souped-up bizarro Ptolemaic system, that I'll be able to use to refute it?
I could just use the Ptolemaic system as is with all its "deferents" and "epicycles," but I'm not sure it could still hold with modern society, which has telescopes (Galileo) and things like TVs, cameras, etc. I need a system that modern society, with all of its current knowledge in astronomy, can use - and still have the sun/moon revolve around the earth.
I saw a throw-away reference in one of my astronomy books with some attempts after Copernicus to still have a geocentric model was to have the earth at the center, the sun/moon orbiting the earth, but have everything else revolving around the sun. Would this even work? Would this model fool my fictional society long enough?
ETA: Confession: this is actually for a tabletop game based on an existing canon so I can't change the existence of the gods or the technology level. Unfortunately one of the player characters is an astronomer so now I need to reconcile the two, which obviously the game creators didn't bother with.