According to Einstein, all motion is relative. So it strikes me that whether you say the earth is moving or the earth is stationary is just a matter of perspective. So for those drawn to the flat earth model because it is geocentric, maybe you can have your cake and eat it too! Just assume the earth is stationary....and also round! Then you do not need to make all of the unsupportable rationalizations for why the sun, moon and stars set, why ships disappear below the horizon and all of that.
Saying the earth is the still point at the center of the Universe is just as supportable as saying any other point is the center. It is kind of like when the train next to yours pulls out of the station and at first you don't know if your train is moving or the other train. It all depends on your frame of reference.
So if you are clinging to the flat earth just because you can't accept that the earth is not stationary and the center of everything, no problem. You can accept that the earth is round, and also all of the evidence supporting the fact that the earth is round, and still hold the view that the earth is stationary. It is just as rational and reasonable as any other view.