If it wasn’t a big deal it wouldn’t have been a paradigm shift. However, it was just a refinement. You’re adding things (relative masses) that weren’t part of this shift, they were later refinements.
The reasons this was a big deal were entirely human. It wasn’t religion: If you can accept the universe as a miracle it doesn’t much matter how God did it; God is just as glorious. It was power: the Church claimed the simpler model was The Truth and saw the new model as revealing a mistake and threatening their power; rather than seeing it as just a model.
And I maintain this was not a refinement of a model.
As a challenge: name one piece of geocentric math that can still be modified by today's practicioners to provide a sensible astrophysical answer.
Static mass is still a useful fact in a world of relativistic physics. But we have not tabulated any facts from geocentric concepts in the last few centuries. No one would even know where to begin or what words to use to even describe them. That material produced from Kuhnian "normal science" under geocentrism had to be thrown out, as there was no way of fitting them in with the new paradigm.
You're shifting the goalposts something crazy. I'd like to point out the original poster talked about refinement in the output of the models, not the models themselves. However, having said that, the heliocentric model is still a refinement (and further refinements, which came later) of the geocentric model. We didn't jump right from geocentrism to Kepler's three laws of planetary motion. The Copernican model still had heavenly spheres as a concept: a concept we don't use today. What you're thinking of as heliocentrism is a refinement of previous heliocentrism which itself was a refinement of geocentrism.
The reasons this was a big deal were entirely human. It wasn’t religion: If you can accept the universe as a miracle it doesn’t much matter how God did it; God is just as glorious. It was power: the Church claimed the simpler model was The Truth and saw the new model as revealing a mistake and threatening their power; rather than seeing it as just a model.