Dear Peter,
there is a venerable tradition of trying to cook up new logics to better describe the world. Dialetheism has a rich history, and there are of course the attempts by Reichenbach and von Neumann/Birkhoff to capture quantum weirdness with modifications to the propositional structure of logic---Reichenbach with introducing a many-valued approach, von Neumann/Birkhoff through weakening the Boolean algebra of classical logic to the structure of an orthocomplemented set. As such, your approach fits right in with that sort of strain.
I'm not completely sold on such ideas. Consider Putnam's classical essay 'Is Logic Empirical?': the question always remains---if it is, how would we assert this? It must be the case that empirical evidence should force us to reconsider our basic laws of reasoning---but that is itself something that depends on those laws: we can only conclude that empirical evidence has a certain consequence by making some sort of deduction from it, but if we question the very principles of reasoning, then that deduction itself would be suspect---so the idea that logic is subject to empirical revision seems to be self-undermining in that respect.
I rather think about this by means of the 'principle of tolerance': different logics are, ultimately, different tools, and may be differently well suited to certain areas. As such, there's not really a fact of the matter regarding any one logic to be the 'correct' one. For instance, it's perfectly well possible to describe inferences in quantum mechanics within classical logic, if one e. g. uses a Bohmian ontology. Since the evidence doesn't suffice to choose between Bohmian and Bohrian quantum mechanics, it also doesn't adjudicate between classical and quantum logic.
That's not to say I'm opposed to such ideas. Studying different approaches to logic has intrinsic value; but I fear that wherever one skirts close to asserting that the 'world out there' follows this logic rather than that one, one runs the danger of confusing map and territory.
However, I think you are aware of this danger---you speak of the distinction between the physical and the abstract and, I think, relegate the logical description to this abstract layer. This is something very close to some of my own ideas---I think in terms of the 'structural' and the 'non-structural', with the former essentially conforming to the abstract realm, the map, and the latter being the territory (in fact, I believe there are interesting issues in that distinction for the philosophy of mind---see my recent article in Minds and Machines: https://link.springer.com/article/10.1007/s11023-020-09522-x).
I'm not entirely convinced by some of the arguments you propose. There might be only one Aristotle, but he can be referred to in different ways---the Fregean distinction between 'Sinn' and 'Bedeutung': so, Aristotle is 'the most well known pupil of Plato' and 'the author of the Nikomachean Ethics', and a sentence like 'the most well known pupil of Plato is the author of the Nikomachean Ethics' expresses a perfectly fine equality of the two 'aspects' under which one might refer to Aristotle.
Furthermore, the absolute identity of quantum particles is something upon which the statistical approach to quantum mechanics is founded---and indeed, if we supposed particles were distinguishable, the distributions we calculate for them would differ from what's empirically observed; only the assumption of their identity makes the predictions come out right.
There is more in your article than I have space here to reply to. Furthermore, many of your arguments seem to be only developed in other articles of yours; I think this article would have benefitted from trying to present as much of a self-contained argument as possible, focusing on a single, clear point you wish to make. As is, I felt sort of lost, with no clear sense of direction.
Still, I wish you the best of luck in this contest.
Cheers
Jochen
