A really bizarre alternate history I threw together:
Galileo has an intense dream in 1612 or as he would later call it a vision. As a result his letter to the Grand Duchess Christina of Florence had a far different tone to it explaining that the heaven in the sky was not the same as the heaven in the Bible. "Look at the shadow of any object and ask yourself 'where is the center?' The heaven in the sky is a shadow of the true heavens."
The Inquisitorial commission looked over Galileo's reply and later debate deciding that Galileo's view had merit but was not simple enough for the average person to understand and instructed Galileo to not present heliocentrism as a physical truth.
Near a decade later Pope Urban VIII and the Inquisition commissioned Galileo to write a work on the two systems. Galileo's work,
Dialogue Concerning the Reconciliation of the Two Chief World Systems, rather then giving arguments for and against heliocentrism as the Pope wanted instead tried to reconcile the two. Despite this deviation from his instructions the Pope was pleased with Galileo's efforts as it solved a lot of heretical issues with the heliocentric system and was somewhat in keeping with the original view that the system was a "mathematical connivance". Yes, heliocentrism was presented as a physical truth but only in the context of the shadow of the true universe God had created.
Galileo's work would be presented as a brilliant merging of the universe being observed and the one of the Bible for centuries afterword even by the rival Protestant religion. Galileo was beatificated in 1652, a mere 10 years after his death as would be said to be the 'man who returned the sword and shield of science to the hands of the faithful.'