More than one thing needs further consideration. First off, SR deals with appearances of electromagnetic phenomena. Second, the speed of light in the vacuum was taken as a constant in the premise, not as something to be proved or demonstrated. There is nothing wrong with SR except that we are using it to limit ourselves. At the same time, putting such a limit on ourselves has historically spurred some to think deeper and wider and pushed our minds to further accomplishment.
That's incorrect. It is a consequence of relativity.
and it also seems to be grossly out of touch with reality and emperical science.
There is not a single experimental result that contradicts relativity. This idea of "gravity propagating faster than gravitational waves" is a null concept, with no basis other than a trivial misunderstanding of what a field is. It's like saying that while you may walk at a finite speed, the ground beneath your feet is infinitely fast.
Something has to be wrong with the picture.
In other words, you don't like it. The universe is the way it is, and not how you would wish it to be.