Except of course that special relativity in its unmodified form applies to globally
flat, Minkowski-type spacetime. Your extension of it using the equivalence principle instead restricts it to applying only piecewise to infinitesimal local regions, and of course we'll need to know something about the overall curvature and establish some rules for connecting those piecewise regions in order to find out what's going on in any macroscopic region. General relativity provides rules for that, and presumably you have some rules in mind as well. So we are
dealing with a modified version. Unless you'd like to show some evidence that the original theory of special relativity involved integrating over infinitesimal local regions of spacetime?