Miller isn’t known for theories; what he did was to run a more accurate version of the MM experiment, and it didn’t fail. That’s fact and not theory and, to my knowledge, that eliminates the basis for relativity.
Science is about theories and measurements. The value of a theory is that it predicts measurements. Measurements are always approximate. But if measurements are close to the theoretical predictions, then it's a good theory.
As far as I can tell, Miller took measurements that seem to support theories about the existence of an ether drift to explain the constant speed of light. Today I don't think most physicists think the ether exists, but it might be worth looking into again. Whether the ether exists or not, relativity is limited in its applications, as Newtonian physics is limited in its applications.