First, I would like to remind you that PhysicsForums is not for personal theories nor for crackpot arguments against mainstream science, there are plenty of other internet forums for that. PhysicsForums is for helping students and others learn about mainstream science. You specifically agreed to those terms when you signed up for your account, and citations of notorious crackpots like Van Flandern are a violation of your agreement. This is simply wrong. The math and how you use the math to make experimental predictions are the theory. So you cannot make math equations fit any theory because if you change the math you have changed the theory.
What you may be thinking of is the fact that you can always produce multiple interpretations of the same theory. I.e. you can ascribe different meanings to the various mathematical quantities. A good example is the relationship between SR and Lorentz's Aether Theory which are both different interpretations of the same mathematical theory, the Lorentz transform. I am not sure if your stance is that the Lorentz transform is correct, but SR is an incorrect interpretation, or if you believe that the Lorentz transform is wrong.
A simple look at history debunks this critique. The first accurate atomic clock was built in 1955. So none of the many experimental confirmations of SR before 1955 could possibly be subject to this weakness. See:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html. There are also many experiments after that time, such as Kuendig's 1963 experiment with a Mossbauer absorber on a rotor, that did not rely on atomic clocks.
Let me be clear here, I am not in any way accepting your critique of atomic clocks, but for the sake of argument I am just pointing out that the success of SR does not hinge on that.