In fact there are already some astrophysicians who create models with varying constants:
http://www.jp-petit.com/science/f300/a301.htm
A - J.P.Petit : An interpretation of cosmological model with variable light velocity. Modern Physics Letters A, Vol. 3, n°16, nov 1988, p.1527
B - J.P.Petit : Cosmological model with variable light velocity: the interpretation of red shifts. Modern Physics Letters A, Vol.3 , n° 18, dec. 1988, p.1733
BTW apart from constant of light, there is also polemic on the very existence of ... Black Holes

J.P.Petit and P.Midy : Questionable black hole. Geometrical Physics A , 12, 2000
http://www.jp-petit.com/Extensions/pres_questionable_en/PQ1trad.htm
As Jean Heidmann, cosmologist at Meudon, now retired, used to say :
- When the talk turns to black holes, you have to leave your common sense in the cloakroom...
Under these conditions, if we decide to forget common sense, where is the limit to unreasonableness? How do we decide to build a "physics of the unobservable".
Quote from harrytrader:
That's the very point of the thread: Walter Shewart, who was a professional statistician who is the father of Industrial Quality Control, has examined the statistical distribution of the 2885 mesurements of light and said that it was doubtful that the mesurements were consistent as for the stability of the variance - that is to say there was heteroscedascity which can be due to the instrument or to real anisotropy. Since he is not a physician he couldn't say. Now Maurice Allais is a Physician that lives today - so that he can use the latest mesurement tools - and as a Nobel Prize, one cannot doubt his intelligence, if he says that the heteroscedascity is real well it's an hypothesis to be taken into account seriously. And since String Theorists from the fundamental point of view is seeing some problem also with a speed of light that is constant this is even more interesting. Now Allais only says that the speed of light varies around the known constant he didn't say that the speed of light can be say double the current constant
.