Test to measure for moving space-time across the earth

Einstein ruled out a particulate luminiferous aether.

However, in A Different Universe, Robert Laughlin writes:

"The similarities between the vacuum of space and low-temperature phases of matter are legendary in physics."

Yes vacuum is not nothing. It has certain properties like permeability, permittivity and even the impedance.
I'm saying it doesn't work the way they predicted. If they're still doing the same experiment then it still isn't going to work. What's wrong with the experiment I detailed in the OP?

Are you familiar with LIGO? In effect (unless I am woefully obtuse!) they implement just such a 'test' as you propose. Given that the base assumption is that both installations would enjoy a 'steady-state' only disturbed by a gravitational-wave event, that would seem to indicate both: A) your fundamental assumption is flawed, and; B) there is no 'observable' aether.