Einstein's 1905 derivation of the Lorentz transformations rested on two fundamental symmetry principles: the relativity principle (dynamical equivalence of inertial frames) and the isotropy of space, alongside the postulate governing the constancy of the speed of light with respect to the "resting" frame.74 The justification of all these principles did not rest, for Einstein, on any a priori notions about the structure of space and time, but was based on "plenty of experiential knowledge" related to mechanics and electrodynamics.75 Later, he would stress that the theory of special relativity could be summarised in one principle: "all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations".76 This allowed Einstein to say that the theory transcended Maxwell's equations, and what he saw as the awkward emphasis on the role of light in his 1905 formulation.77 Special relativity is essentially a constraint in the sense that a symmetry is being imposed on the fundamental equations of all the non-gravitational interactions.These EInstein opinions are from 1940 and later, long after that 1905 paper.
The principle that all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations was written by Poincare in 1905 and Minkowski in 1907, but not endorsed by Einstein until about 1915. If that is really the essence of special relativity, then all the credit should go to Poincare and Minkowski, as Einstein contributed nothing to this line of thought.
This is the biggest reason I believe Einstein should not be credited with the discovery of special relativity. It is not just that others had the formula earlier. It is that the essence of the theory is Lorentz covariance, and Einstein did not even understand the concept until many years after others had published it and gained widespread acceptance.
The Brown paper does have a good discussion of the history of Noether's theorem. Nowadays, conservation of momentum and energy are considered synonomous with symmetries of spacetime. This was one of the most important insights of XX century Physics.