The bit about Copernicus inaugurating the scientific revolution -- is that an error, or part of an example-from-argument that I should have been quick enough to catch?
My understanding is that De revolutionibus was ignored when it was published, and didn't start making waves until the 1600s. This fits with your point that no one knows what science knows -- except that in this case, Copernicus can't properly be said to have known what he knew, either.
As I understand it, the secular Saint Nicolaus thought he had found a neat trick for computing where planets would appear in the night sky, which was sometimes more accurate that the Ptolemaic model (ellipses > Fourier series epicycles > circles). He may have believed in a heliocentric universe, but given the evidence available to him at the time, his view could have been no more true than Newton's corpuscular theory of light.
It seems un-Bayesian to give much credit to Democritus.