As I said, according to Einsterin, Hoyle, Born and Ellis, geocentrism is equivalent to geokineticism within GR and coordinate systems. To argue that there is some physically significant difference is to argue against GR.
"You obviously cannot answer the question because nothing we have any experience with COULD exert force upon the Sun to move it around the Earth while leaving the Earth motionless. It must be magical forces, that idea has a long and storied past, but it isn't Science."
As I said, it is the wrong question. No magical forces are involved and it is the science of GR and coordinate systems according to Einstein, Hoyle, Born and Ellis.
I think that the Ellis quote is especially appropriate for this conversation. Your objections are purely philosophical, not scientific. It's fine to have philosophical objections, as Ellis notes below. It is no benefit to science to pretend that your objections are scientific when they are philosophical, as he also implies.
"People need to be aware that there is a range of models that could explain the observations,” Ellis argues. “For instance, I can construct you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations.” Ellis has published a paper on this. “You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that.”
Ellis, George, in Scientific American, "Thinking Globally, Acting Universally", October 1995