Before I continue I want to point out that empirical observations really are agnostic about the existence of a preferred reference frame... In particular, if we imagine designating one reference frame to be the true reference frame then, relativity itself, tells us that applying the laws of physics in that reference frame has to give us the correct results.

What does it mean that this preferred reference frame "exists"? What about general relativity? I don't even understand what a "preferred reference frame" means there mathematically.

To make it even more plausible that there is some true rest frame I will remark (but not argue) that relativity is a pretty general phenomena that can be derived from any model that conserves momentum, where the forces obey the inverse square law and all propagate at a constant speed relative to some fixed background, matter is held together in equilibrium states of these forces and time is implicitly measured via the rate it takes these forces to propagate...

I have no idea what you're talking about. Generally speaking, I would refrain from inventing new physics before understanding the physics already invented in the last 100 years.

Regarding the paradox, the correct thing is summing over different reference frames weighted by 2^-{Kolmogorov complexity}. See also this and discussion here.