Actually there are experimental ways to test theories with varying speed of light. One of the consequences of these theories is that the electromagnetic coupling constant [itex]\alpha=e^2/2\epsilon_0 h c[/itex] does also vary. This constant determines for example the spitting of the spectral lines of the hydrogen (the “fine-structure”). Comparing distant spectral lines with the ones of today might provide information about a varying [itex]\alpha[/itex].