There's another problem that I think needs to be addressed. The speed of light is defined as a constant nowadays, so it's not something that can be measured with current time and distance standards. One would be in the position of using a standard that was calibrated by the appropriate national standards laboratory (NIST in the United States) based on the current standards which assume that the speed of light is a constant to measure the speed of light. This is highly circular.
One way of addressing the issue would be by acquiring some old "retro" standards of the meter that are not based on the current SI definition of the meter. This means that the aspiring experimenter may not be able go to their local national institute of standards to calibrate their standards used to measure distance (whether it be flight distance or wavelength) for such an experiment. They would need to use a different standard (I would assume they would use the old standard based on the prototype meter bar standard, but I'm not the one interested in doing such an experiment). More importantly, beside using such a standard, they'd need to
describe what standard they were using in some detail.
If they only wants to compare the speed of light from a moving source to a speed of light from a stationary source in a differential measurement, this obstacle may be avoidable. Such experiments have been done, some of the cosmological tests described in
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#moving-source_tests for instance. The cosmological tests are well known and inherently use such a differential measurement technique to compare the speed of light from a binary source (such as binary star) moving away from us to the speed of light from the star moving towards us. The effect on the image of any change in the speed of light based on source velocity is discussed in many textbooks as well as in the papers referenced in the above link (though I don't recall the details of exactly which textbooks). I'm not familiar with the details of the terrestial experimetns described in the above references, they may not be described in textbooks either, which means one likely has to read the papers for details.
The fact that our primary standards have been calibrated from atomic clocks and the speed of light for quite some time should be a big clue that such an experiment is not likely to yield any unexpected results, given the number of highly precise experiments which have been carried out successfully using references traceable to the NIST standards, said standards being based on the constancy of the speed of light.
It could be interesting to find the meeting notes of the professional body, the BIPM I believe, where the change in standard was discussed before being adopted. I'm sure I've read something about this once upon a time, but I don't recall the details.
