Cahill Analysis of Interferometer Experiments, Input?

[The victorious truther]

So i've been arguing with someone on ResearchGate regarding Special Relativity and other caveats related to his own pet Aether theory. He is, as many of these non-mainstream critics of Special Relativity are, a big fan of specific interferometer results from the late nineteenth or early twentieth century as he supports his theory on the back of a re-analysis of previous results. He claims that any vacuum interferometer will give a null result and that interferometers with a medium for the light beams would then give a non-null result. Something that was analyzed in this paper here: https://arxiv.org/pdf/physics/0205070.pdf. I'm curious about what your perspectives on it are given the derivations from their initial assumptions seemed to check out. 

If you could find a resource(s) for Lorentz Violating experiments conducted in a medium i'd heavily appreciate that. I had found a few that I thought had a relation to this such as https://arxiv.org/abs/0706.2031v1. 

His own paper is given here: https://www.researchgate.net/publication/350770907_MM-Cahill

The key idea is that this analysis combines both Lorentz contraction and the idea of light having a different speed in a chosen medium of 

\[ V = \frac{c}{n} .\]

You basically then perform the same analysis to determine the time difference between a path in the direction of motion and the path of the interferometer arm perpendicular to that. Which comes out to be 

Compared to it without the Lorentz contraction taken into account