How can you extrapolate so much from only 300 years' data?
Setterfield: As far as your question is concerned, several points need to be made. The basic cause of changes in the speed of light and other associated atomic constants is a change in the strength of the Zero Point Energy (ZPE). The ZPE governs the properties of the vacuum, so any change in the strength of the ZPE will bring about changes in vacuum properties. These changes result in variations in the associated atomic constants.
It is true that we only have about 300 years of data for the speed of light, and just about 100 years of data for other atomic constants, but we do have about 3600 years of data for the behavior of atomic clocks when their dates are compared with orbital dates. But to go back to the origin of the cosmos requires a different data set. These data come from astronomy, knowing that atomic orbits are sustained by the ZPE in a manner explained by Puthoff, Haisch, Boyer, Spicka, de la Pena and others. When this astronomical data is considered, we have data right back to the origin of the cosmos. The equation from that data set gives us the equation for the way the speed of light has behaved, how the atomic clock has behaved, and how the ZPE has behaved since the beginning. That is all explained in my invited paper, Zero Point Energy and the Redshift, presented at the Natural Philosophy Alliance conference,June, 2010.
Quite apart from the observational evidence, a very similar equation can be derived theoretically for the behavior of the ZPE from first principles knowing how the ZPE originated. This has been done twice; once by proceding backwards from the astronomnical equation to verify the equation for the physical events that originated the ZPE, and once by proceeding forwards on a different basis from the starting conditions for the ZPE to derive the final equation. Because of some perceived problems with both approaches, I have yet to produce a final rigorous version, but that is more a matter of time than anything else.
As far as momentum of photons and similar considerations are concerned, some evidence comes from the fossil record, where plants grew faster and larger than today. For example the 'horsetails' which grow to about 2 feet today grew to over 60 feet in the Carboniferous. Similarly, invertibrates and vertibrates both grew larger than today, which is why giant forms are found there. Thus giant scorpions attained the length of 8 feet, while dinosaurs were up to 80 feet long. Today, these creatures could not function; it takes too long to get a message from their tails to their brains. The basic science for these comments can be found in our publication The Bible and Geology. The more extended explantion is in the paper, Zero Point Energy and Gigantism in Fossils. So there is evidence from astronomy, paleontology, as well as botany and zoology to support the contention. And some of this is electrical as the electric properties of the vacuum were different. See my paper, Reviewing A Plasma Universe with Zero Point Energy.
NOTE: Cosmology and the Zero Point Energy, published 2013, contains all relevant material dealing with this question.