Perform the two-photon muonium 1S-2S transition measurement in ultra-high vacuum, then repeat in a chamber at 1 atm air pressure. Utilize existing setups at PSI or J-PARC. Observe any frequency shift in the gas-filled case. A downward shift would indicate radial compression from gas atoms, shortening measurement rulers microscopically and causing clock drag - consistent with the density squeeze model. This matches the clepsydra pressure cap. No quantum effects required.
Boris Karagiannis (Sun,) studied this question.