“if your little chair is stationary, then that would effectively make the earth the center of the universe.”
No it would make my little chair the center of the universe and the earth would be revolving around me.

“even then, parts of you would still be moving through space.”
relative to what?

“also, if you traveled at the speed of light and appeared to an outside observor to not be traveling through time, you would still appear to be traveling through time in your own frame of reference. not moving through time would only be an optical illusion.”
Wrong. Look up the Twin Paradox.
You could respond with the technicality that no matter can travel at the speed of light so you would still travel through time, just very slowing. We could however get arbitrarily close.

“you would be moving through space relative to the rest of the universe.”
No the rest of the universe would be moving relative to me. There is no absolute frame of reference. You’re free to choose any coordinate system that conserves all observables.

“and what does the twin paradox have to do with it?”
Special Relativity. Time dilation. Time is slowed by the reciprocal of the Lorentz factor. epsilon = sqrt(1-v^2/c^2). Set v=c and time stops. Like I said, look it up.