With all due respect, light measures c in the stationary frame, so length contraction and time dilation make absolutely no difference to this calculation.You keep saying this. It is not true. (And the reference you claimed supported this said nothing of the sort, which is rather annoying).
The speed of light is assumed (actually, defined) to be the same in all directions, not measured to be the same. Indeed, in a world with length contraction and time dilation, it is impossible to measure the one-way speed of light.
GPS shows light measures c or it would not work. That is why the link is valid.
Allan et al., IEEE Trans. Inst. and Meas., IM-32 no. 2 (1985), pg 118.
They discuss in detail how time and frequency comparisons among the various standards organizations of the world can be performed with an accuracy of about 1 part in 10^14, using GPS satellites.
Obviously, like MMX, frequency deviations would indicate a measured speed of light that is not c.