@layman,
I don't know what you mean by the term "physical reality". Sciens deals in what is testable and confirmed by experiment or observation. Your use of "physical reality" seems to add something that goes beyond science.
Yes, theories in physics are adapted an expanded to match new experimental results. This is not a weakness. This is one of the strengths of physics.
If you listened to or read the rather insightful Feynman talk on Mathematics and Physics, there are a great number of Physics laws for which we have found no explanation other than the mathematics (Feynman uses the Gravitation inverse squared law as an example).
So, I don't know what difference you are making between theory and math. The theory of Relativity is expressed in Mathematics (at least now in 2017 we have no other way to express these theories.) When you talk about red shift, and expansion into 4 space, and velocity transformations you are talking about mathematics. If you are going to reject this... then this talk of "red shift" is non-sense. Talk about the philosophical "facts" using philosophical ideas rather than mathematical ones.
But you are wrong about facts. These mathematic theories are objectively testable. You can use them to make predictions that you can then confirm with careful measurement. Of course, when these predictions fail (as they sometimes do) the Physics community works to revise and improve the theories.
But time and time again, Relativity has passed the test. It has make some pretty impressive (and counter-intuitive predictions) from cosmic rays, to gravity waves.
That is why it is accepted by the Scientific Community... in spite of the fact it upsets some philosophers who are looking for something more than testable mathematics. But what the philosophers are looking for isn't mathematically testable and therefor it isn't science.
And the "facts" you are looking for aren't science either (as long as they contradict the mathematical model that has been tested, confirmed and accepted by the scientific community).