And yes, it does matter where you select the “stationary” center of the universe. Moving bodies still have limited velocity.
I do not understand the point you are trying to make. Of course moving bodies have limited velocity. Even light has limited velocity.
Suppose we picture the universe as a stationary bicycle floating in a perfect vacuum of space, but the pedals, sprockets, axles, and tires are moving in normal but perpetual bicycle-like motion. We could reasonably argue that the “stationary center” of such a universe was the center of gravity of the bike, regardless of the rotation of its various components (the location of the “center” would actually fluxuate a bit, moving in a tiny circular pattern, but let’s ignore that for now).
Suppose that an ant were on the seat of this bike. He would perceive that he and the frame were perfectly stationary (and he would be almost right), but the driveline and wheels were spinning.
Now suppose we suddenly hammer a nail into one of the tires, such that it is unable to move, but the motion of the driveline does not change (so the whole bike is now spinning around the stationary wheel, instead of the wheel spinning within the stationary frame of the bike). Suddenly (to an outside observer), the whole bike would be spinning in a crazy fashion around this fixed point. Yet, the ant on the seat would still not perceive any difference. His relationship to the parts of the frame has not changed, and his relationship to the driveline and wheels has not changed. Assuming the ant cannot perceive any change in inertia or rotational velocity (which would be the case if the ant was “born” in this state), nothing has changed. The handlebars have not gotten one millimeter farther or closer. To an outside observer, the handlebars are now spinning around the ant (which appears as but a dot), but the ant is spinning at the exact same rate and cannot perceive any change. The “stationary” wheel seems to rotate at the same speed (even though it is really the ant who is rotating around the wheel, according to an outside observer). The other non-fixed wheel remains at the same distance and is spinning at the same velocity as it had always moved.
It is impossible for the ant to know if his bicycle universe is “anchored” to its center of gravity, or to a random point on any of its components (which might happen to include the very spot on the bike’s seat where the ant happens to be observing the bike).
Welcome to the Special Theory of Relativity (my reference to a “center of gravity” was illustrative. I do not mean to actually throw gravity into my illustration, and delve into General Relativity, and be cursed from the Beyond by Richard Feynman).