If I'm not wrong, the clocks ticking non-simultaneously in another frame will make the experiment null.
Do you think we could use a radar gun to test RoS?
We know enough about time dilation to account for any difference in the rate of clocks in different frames. We could even use the same technology used in the GPS satellites to keep clocks in different frames ticking in sync... That would decrease the absolute accuracy some but, the accuracy should still be enough to determine a variation in the timing of two events as measured from two frames.
You could also use a variation on the M&M experiment. You would not know the absolute timing but by measuring the interference pattern of light from two sources, you would be at least confirming the relative simultaneity of the two events. If the interference patterns vary the events were not measured to be simultaneous in both frames... And yes this would require some controls to establish first how the two interferometers record two remote events when the interferometers are co-located...
But given today's technology and accurate atomic clocks. One could design an experiment such that two remote flashes are initiated from the midpoint between the two... Confirmed by flipping a switch and then measuring the flashes to be simultaneous. That establishes the rest frame of the flashes and simultaneous detection at the midpoint between the flashes. Using a fiber optic trigger mechanism the time from flipping the switch to the flash(es) could be known. Knowing the delay from the trigger and the flashes, the experiment can be redesigned so that a moving detector triggers the device such that the flashes occur when the two detectors are next to one another. The stationary detector would detect the flashes simultaneously, while the moving detector would detect the flashes sequentially.
If CERN can measure the velocity of neutrinos to billionths of a second... The only real issue is that this can only be acomplished in vacuum and with distance or velocity that makes it impractical, in atmosphere. Satellite tests have been proposed but they are expensive.