Ok, I confess that I didn't read the entire comment. But you have a second problem, as you should explain why the conventional explanation does not hold or is canceled by your theory.
I'm already convinced[0] the effect is small, if it exists at all. However I thought of another experiment that might be easier to perform, to see if there is any effect at all: take two crystals, as similar in depth as one can make them, with two different isotopes, and measure the difference in index-of-refraction. Silicon (28 and 30?) would probably be good for this, as would laser interferometry. (Maybe the Gravity Probe B people have some extra pure isotope wafers they'd be willing to lend?) If I'm right then the Si-30 sample will have a slightly larger index of refraction than the Si-28 sample. Someone needs to do the math though because if the effect is far less than like one layer of atoms, or a few impurities here and there, then the experiment isn't worth doiong.
Isotopes are not 100% chemically equivalent and they form chemical bonds with different vibrational resonances because the vibrating masses are different. You can see those differences in spectroscopic line shapes including in refraction (which is related to absorption by the Kramers-Kronig relation). My guess is that those effects would swamp out any relativistic ones by a lot, and because you can't tune the isotopic mass you wouldn't be able to isolate a gravitational effect.
In fact it appears that the isotopic dependence for silicon isotopes is known,
Perfectly applicable paper, thanks! I skimmed it, but I didn't see an explanation for the lower refraction index for the heavier isotope. It had the lower RI at all wavelengths they looked at. I think it's useful to ignore the "phonon resonance" wiggle in the middle of their tested range on page 4, around 600nm, if looking for some other effect. (it's crazy that an electron that weighs like 10^-31 kg could actually jiggle a crystalline lattice to the point you can see it at all, but I suppose there's a lot of electrons, and Tacoma Narrows bridge reminds me of how powerful resonance effects can be).
which have very far reaching effects in term of refraction (the real part of the permittivity decays as 1/w).
In term of resonances, it's important to note that the nuclei themselves are not neutral either. In the IR, the time dependence of the field is slow enough that the nuclei can follow it resonantly. Those fields are much below electronic resonances so the electrons aren't even contributing much beyond making the crystal stable!
