Uniform rotational velocities cannot be so transformed. Nor can accelerations. However uniform relative velocities do not describe much physics so that any theory limited to relativity is of very little use in terms of general problems. The invention of General Relativity was a recognition of this difficulty but unfortunately it does not allow treatment of much physics either because of the Riemannian geometry and the notion of curvature. Now to some of the points raised in your paper.
Furthermore space has no properties whatsoever.
I have two more papers coming out next year, on the fundamental particles, the other on absolute velocity kinematics to replace both relativities. The preparation for all of this was set up in papers already published in Physics Essays. I believe that the only solution to the illogic found in both relativities is to produce a kinematics which will allow unification of cl. Electrodynamics and cl. Quantum Theory into one consistent whole.