^ Well, let me crunch some numbers.

If there was a galaxy moving in translation at 300 km/sec (3.0e5 m/sec, or 0.1% of C) then the lead angle for the light rays should be asin(0.001) or 0.057295 degrees, which is 206.264 arc seconds. If half of the photons actually travelled at 299e6 m/sec their lead angle would be 206.954 arc seconds, a 0.69 arc second difference, which should be observable with current telescopes, a bit like gravitational lensing.

I don't know if that's a valid way to look at it, but if it is it would at least set a limit on how big the effect could be.