Martin Luther was a contemporary of Copernicus’s, which is fascinating.  I have to wonder if you think Copernicus may have gained any courage to promote his theory from the example set by Luther of challenging authority and seeking to change the status quo.
Only indirectly from Rheticus, because Luther published his 95 theses in 1517, so there was a lot of time for Copernicus to learn what was going on and to be motivated if he were going to be motivated by Luther’s actions.  But he didn’t do anything.  It really took Rheticus and not only their conversations but something that I did not include in the play, which was Rheticus’s publication of a summary of Copernicus’s ideas and the response to that summary, which really convinced Copernicus to go ahead. 

I know it’s impossible to answer what-if questions about history, but based on the research of later men like Tycho Brahe and Kepler and Galileo, how might we imagine the progression of science playing out if Copernicus hadn’t been convinced to publish?
One thing that would have happened is that Archimedes’s account of Aristarchus would have come to the attention of mathematicians within a few years of Copernicus’s death.  So people would have known that there was an Ancient Greek idea about a Sun-centered universe.  Kepler might have figured out, with the pattern he saw in Tycho’s data, what was actually going on, and once Galileo saw the moons of Jupiter and could demonstrate that the Earth was not the only center of revolution, then the time would certainly have been ripe.