Yes, good point. Also, classical electrodynamics based on Maxwell's Equations was already known to be Lorentz invariant, not Galilean invariant, so SR can be th

Yes, good point. Also, classical electrodynamics based on Maxwell's Equations was already known to be Lorentz invariant, not Galilean invariant, so SR can be thought of as simply taking the invariance properties of electrodynamics and "porting" them to mechanics (whereas pretty much all other approaches went the other way, trying to "port" the invariance properties of Newtonian mechanics to electrodynamics).