Dear Sergey,
You are absolutely right. Time reversibility is not fundamental. The recent XXI Solvay Conference on Physics has been devoted to fundamental irreversibilities in Nature. The proceedings have been published in the volume 122 of Advances In Chemical Physics. The section four, titled "Extension Of Quantum Theory And Field Theory" contains irreversible extensions of the simple time-reversible equations. For instance, an extension of quantum field theory to study unstable particles in quantum states outside of Hilbert space was presented. My own work on the arrow of time must be considered a generalization of the dynamics of correlations developed by the Brussels-Austin School (pages 261-276 of the proceedings).
I am happy to find in this contest so many people that agrees that black holes are only a mathematical idealization. The idea behind strong gravitation is particularly interesting to me. I have read something about the analogies between strong gravity and QCD, but my knowledge of this topic is very superficial. Your remark of that it is related to a Lorentz-invariant theory of gravitation has increased my curiosity and I wait to learn more about this subject in brief. Thank you for the link.
Regards