You wrote " For instance, it the speed of light slows over time, we would expect redshifting of distant light sources, and we would also expect that the CMB radiation would be relatively uniform in temperature. "
The cosmological redshift is a loss of energy, but the speed of that faraway light is the same as the light from from our nearby sun. Now, I'm guessing you're thinking of it in terms of 'old light' relative 'young light' there, right?
Which then might mean that light coming from billions of years ago should be slower than light coming from a 'newborn' source, some eight nine light minutes away? Am I getting you wrong there? Or maybe you're thinking of it as some invisible 'field' of molasses slowing everything down equally? In which case a cosmological redshift becomes irrelevant unless you think of it as the mainstream proposition do, as a result of a expanding universe. =
Rethinking. If you meant that we have slower 'light' now it become slightly confusing for me? An alternative would be to consider light coming from different 'time zones' relative your observation. That would then give a universal 'golden standard' and you could then prove relativity wrong just by moving your observation some light years, to find yourself in another 'time zone'. Which indeed would wreck havoc not only with relativity but also with most of the foundations of physics. This last one would be a interesting universe and should be finite as light has to 'stop propagating' at some defined 'age/distance'. Kind of like that one
Douglas Adams would have liked it I think :) or maybe the rights for it should go to the disc worlds?