Your early history of relativity isn't quite correct. The experimental results posed no convincing challenge to the established theory. After all, Lorentz' theo

Your early history of relativity isn't quite correct. The experimental results posed no convincing challenge to the established theory. After all, Lorentz' theory of ether contraction in the vicinity of moving bodies (the exact same mathematical operations that we today see as a fundamental building block of special relativity that still go by the name Lorentz contraction) could adequately explain those experiments (the maths is exactly the same as for a relativistic interpretation, yielding the exact same predictions for all experiments possible around 1900). What motivated Einstein's work (and that of other, less successful theoretical physicists at the time) was the mathematical impossibility of classical mechanics and classical electrodynamics both being correct at the same time. After all, his paper that introduced special relativity was called "on the electrodynamics of moving bodies." There were no mirrors involved.