Regarding homogeneity of spacetime, you might be interested in the fact that relaxing that requirement leads to a Hubble-like constant, and hence a cosmological constant. These constants then become slightly less of a mystery -- by which I mean they become the same kind of mystery as the speed of light itself. This paper by S. Manida sketches the derivation of the associated extended Lorentz transformation, and shows how a new universal length constant arises.It's symmetry that determiners everything really.
But... I won't say any more about that here since it's a bit tangential to the topic of this thread, which was about standard SR.