Suppose the speed of individual photons reduced over time. Would that explain the apparent speeding up of distant galaxies? The observation that distant galaxies seem to be speeding up has led to the theory of dark energy.
However if the speed of individual photons actually reduced over ( very long ) periods of time wouldn't that also offer a valid explanation? 
What if we postulate that the speed of newly emitted light and other electromagnetic radiation is c but slows at a constant microscopic rate thereafter.
I would hazard a guess that all our measurements of the speed of light have been made using new, fresh light as it were. has anyone ever measured the speed of the light exclusively from the farthest galaxies etc?
 A: The speed of light from distant galaxies has been measured, and it is (as near as we can tell) precisely equal to c.
More specifically, by radio telescopes (treating 'radio' as a form of 'light' since they are both electromagnetic fields and both show the same observed redshift behavior when looking at distant galaxies).
A radiotelescope like the VLA has an array of radio antennas spread at large distances.  By looking at the difference in time of arrival of the signals from one antenna to another, they can tell where the radio signal is coming from.  If the source is to the East, then the easternmost antenna gets the signal first, etc.  They can use this to determine positions to about a millionth of a degree (a few milli-arcseconds), and the position matches up to what optical telescopes find.  This would not be possible if the radio signal were traveling at an unexpected speed.
Footnote: radio waves don't travel through space exactly at c because space isn't a vacuum.  But this is a very tiny effect, and when you correct for this, it still works.
At the other end of the spectrum, the same technique is used to find the direction to gamma-ray bursts using detectors spread across the solar system.  (Gamma rays are also electromagnetic waves.)  These are some of the most distant objects ever observed (redshift factor can exceed 6) and it still works.
A: Speed of light $c$ was defined as a standard unit, thus it's impossible for you to consider such matter in orthodox physics. People chose this way from the solution of wave equation.
However, to answer your argument(assuming $c$ reducing over time and keep the rest of physics untouched.):
Suppose that speed of light slow down over time(with respect to "meter" in the sense, a physical objective scale.), as $c(t)$, then... wolfram did not have a general solution. Thus we suppose that, since the acceleration was over a long period of time, thus it might be sufficiently approximated by Laurent series of some finite order. Expand $c(t)$ in terms of $x^a$ where $a$ an integer and solve it independently. For a full solution, you would encounter higher frequency dominance in nearby spacetime neighborhood and a lower frequency dominance in far spacetime neighborhood. If one only takes half of the solution, then you would still be able to pick a rather violent oscillation (but may be approximated to be smooth as it comes from a large distance) in the amplitude in a mid-range, but, you would receive a reduction in frequency as a response to redshift. 
After all, if you want to prove the solution works or not, you need to test and make comparison from GR: which solution would give a more precise description, if you could actually obtain one. 
But I thought there's something wrong with just assuming the reduction of speed of light, i.e. near the black hole, the time slows down, thus the reduction of speed of light must be different, which would make $c(t)$ to be dependent on $x$ as well. But then you would basically throw away all the physics you've learned from high school, and you would effectively obtain faster than light phenomenon through light. 
Reducing light speed may be helpful to think about some none conservative phenomenon, but it also break up the usual structure established by SR, as light speed was at the central of it's configuration. Thus, it's possible that the solution including the reducing of $c$ may change the topology of 4 space and thus become invalid. 
A: I think we define distance by light signals, so perhaps the answer is yes, and perhaps the two are in a way equivalent.
On the other hand, the CMB shows us that the size of the fluctuations on the celestial sphere have stretched since the CMB was released. According to what you are saying, while the photons would indeed redshift as explained by user9976437 in their answer, these fluctuations should not, at least naively.
Not to mention that there are many other observables predicted by the standard cosmology that you would no longer be able to predict unless space is expanding.
So I don't think it's a good solution.
I think it's good that you are questioning the standard model of cosmology, and we should all do so, not believe things blindly.
