Well, there's a few things to unpack here, not least of which is that none of the heliocentric models at play were Galileo's. More can always be said on the matter, so if anyone would like to make their own writeup about our favourite grumpy old Tuscan disputant; for the meantime, we do have some previous threads covering that kerfuffle about the cosmologies:

• u/link0007 addresses a much similar set of questions to yours here;
• u/restricteddata here points out that Galileo, in fact, did succeed in killing an old geocentric model;
• and u/MannyStillwagon notes the difficulty of measuring parallax, which is relevant to the problem.

Some bonus restricteddata on related matters:

• Why Galileo ran afoul of the Church;
• On why Copernicus preferred his heliocentric model (not the first or the last time anyone's done something "for the a e s t h e t i c").