How do you synchronize the clocks and compute the measurement, without depending on the conclusion?

You run into a similar problem with Michelson-Morley: because the apparatus and the light both get distorted by any motion, you can’t even in principle detect the aether wind with interferometry. You need a non-comoving dynamic source, eg, LIGO with black hole collisions.

Their one-way experiments seem to require similar, ie, we can observe dynamics but cannot measure a static bias.