Like, if you could stand above the solar system and look down on it, the Copernican model would say it makes more sense to hover over the Sun and imagine everything rotating around you than to hover over the Earth and imagine everything rotating around you while pirouetting .

This is an interesting point. What does "more sense" mean?

From a purely utilitarian point of view, Tycho Brahe's compromise system is as useful as Copernicus's: it gives the same experimental predictions while still keeping Earth at the center of the universe. Kepler's acceptance of the Copernican system had more to do with his Pythagorean views, his perception that the center of the universe must contain the Central Fire, the cause of all motion.

In other words, we're dealing with subjective views here. And yet it objectively seems to make more sense to center the Solar System around the Sun. Perhaps because there is no reason to privilege Earth above the other planets, and no reason to assume that the Sun "really" revolves around, say, Venus?