I'm just wording what I say to egg you on into making an arguement over someone else's much more complicated, far easier for you to explain, experiment.
So you are just trolling?
Do you actually understand what your experiment actually entails? What the path of the light will be which you would be measuring? All the timing involved?
Because without a medium to the universe then any point may as well be its center, and if Earth is the center then we look bad having not yet proven that everything in the sky revolves around us. Ahh but then Einstein came up with relativity where the motion of an object is only relative to an observer.
That literally makes no sense at all.
With or without a medium you have the same issue. It doesn't magically make a centre.
All a medium would allow is a hypothetical absolute reference frame, but that would rely upon the medium to be static (e.g. it can't move relative to itself).
But this absolute reference frame doesn't make a centre. Without this medium it still doesn't make sense for any point to be the centre.
If you do want to pick an arbitrary point as the centre (such as where Earth is now), you can't just have that point to stick to an object. The object would be able to move away from the centre.
So if you decide to pick where Earth is now as the arbitrary centre point, then Earth will move away from it as it orbits the sun (and other factors).
And you need to distinguish between rotational and linear motion.
All linear motion is relative. The speed of light is constant in any inertial reference frame, where these frames just undergo linear motion.
While some aspects of rotational motion are relative (e.g. it wouldn't matter if the stars rotated around us or Earth rotated, it would look the same), other parts are not, such as the Sagnac effect and the Coriolis effect.