Vesselin
I agree strongly with your emphasis on philosophy - but philosophy is mainly rhetoric; therefore subjective. Logic is also important and less subjective.
You emphasize the physical reality of the four dimensional continuum and that this was somehow "proven ? " by Minkowski & Mermin. One cannot prove physical reality; one can only observe/measure it. Minkowski can't, and Mermin can't, prove it is 4D. They can express their philosophical preference for a 4D representation.
ALL measurements are in the "NOW". It is impossible to measure Duration (see the winning essay of the previous competition). Measurements of duration are actually measurements of spatial changes of configuration, e.g. the sun was there at that-now, now its here at this-now. We can of course map multiple nows to an extended time if we find that useful mentally, but we cannot observe such a thing.
You write "Unlike Poincare, Minkowski appears to have realized that special relativity, particularly relativity of simultaneity (which IMPLIES the existence of MANY spaces) ..." etc. - my emphasis.
The logic here is faulty. Special Relativity mandates that because of a finite velocity of (electro-magnetic) observation = physical experience, each observer (unless co-located like quantum superpositions) has (a) a different observable part of the same one physical universe, and (b) each observer's measurements of the same events will differ. However SR also mandates that because of the constant speed of e-m all the different measurements can be rationally correlated by the Lorentz transforms so that their is no conflict, i.e. all observers are observing the same set of absolute events = the same space or universe.
So it is OK in SR to assume there is one common space that we all exist in (don't we ? ) - BUT it is not possible to impose one absolute co-ordinate system (preferred observer). SR gets rid of absolute space but not our shared space. That is why he called it a theory of Relativity. Scientifically our measurable experience of the same universe is relative to the observer.
Taking Minkowski's logic for empirical reality is not a philosophic choice I could - reasonably - recommend. That it is very useful mathematically is - rationally - very true.