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*PINK MATTER ALERT*

Well if it did slow down (perhaps even go in reverse) and then sped up, what does this say about the cosmological red shift assumption?
Wouldn't it be simpler to explain this all as the universe not really expanding (though it is moving about), but rather that the speed of light may have changed with time and location. It's a big assumption that the intrinsic impedance of space is the same all over for all time.
The cosmic background radiation may just be light that is absorbed by the matter (and there's lots of it) between the heavenly bodies and reradiated as heat. It may not be the left over light from the big bang doppler shifted.

Well if it did slow down (perhaps even go in reverse) and then sped up, what does this say about the cosmological red shift assumption?

The Red Shift is not an assumption.

What you are discribing has nothing to do with the "speed" of light, it has to do with its frequency, or wave-length, as seen by a distant observer. When a distant object is moving towards the observer at a significant percentage of C its wavelength is compressed, or shortened, appearing blue to the observer. As a distant object moves away from the observer its wavelength is expanded, or lenghtened, appearing red.

This shifting towards red or blue would happen regardless of the measured speed of C. Since E=MC2 works well enough (to as many decimal points as we can measure) that Hiroshima was vaporized, I respecfully suggest that Einstein was closer to the correct answer than any fanciful idea that C is not a constant in a vacuum.

Remember Occam's Razor: A rule in science and philosophy stating that entities should not be multiplied needlessly. This rule is interpreted to mean that the simplest of two or more competing theories is preferable and that an explanation for unknown phenomena should first be attempted in terms of what is already known.

It may not be the left over light from the big bang doppler shifted.

What I'd like to know is how, in an expanding universe in which light moves at a constant speed and throughout which nothing can move faster than light, any electromagnetic radiation "left over" from the Big Bang that is not the artifact of an almost infinite series of reflections can be observed by anyone who has not been moving at the speed of light from the very moment of the Big Bang. Based upon the proposed rate of expansion and the age of the universe, for distinct point sources of light what is the upper limit on the oldest image that could be expected to be seen?