You have a few misconceptions here and I hope you don't mind me elaborating; we usually agree on most issues, but I do think this is important.
Coepernicus had JUST finished his work on planetary motion. It was new. Before that, if anyone started babbling on about the earth around the sun, people would be like "how do you know?" and they'd be right to - because what they didn't know about was elliptical motion. Without a knowledge of elliptical geometry, it was just as weird and convoluted to have the earth going around the sun as the sun going around the earth. But after Kepler published his laws of motion, anyone could run the numbers and go "holy hell! That is so much better!" and that made people eat it up as truth.
They would have told everyone. The town around the observatories would have been proud of this. The German clergy loved a chance to stick it to the Catholic establishment and would have pushed it from their pulpits. The Vatican tried to make an example of Galileo and they got to him, but his publications on the phases of Venus had already spread: Venus does not have phases in the Ptolemaic universe, only in the Capoernican one.
And because the position of the earth around the sun has implications on agriculture, farmers knew about this. Because the position of the moon around the earth has implications on tide, mariners knew about this - sailors are always the first among laymen to implement new technologies! So no, it wasn't restricted to the schooled kabals. It took relatively little time for the Catholic Church to find themselves defending a position that was just obselete: it was too useful, too simple, to buy the evidence that the earth goes around the sun.
And this is my point: if the 90% isn't waking up to something, there's a punch to your evidence that you are missing. There is a punch to the evidence that should be there if you have truly found a hard truth.