One of your best essays. You think big!
You note that "maths is proving unable to model and predict the complex physical universe." I fully agree with this but I don't know that it is math, per se, that is the problem. I believe it is projection of inappropriate mathematical structure onto the physical universe that is the problem. This is true in almost every field of physics, but let's focus on one in particular. You state
"clearly no excluded middle exists in reality, or 'nature'. Binary maths is then metaphysics, an 'approximation' of nature."
This 'qubit' approximation works well enough statistically when large numbers of spins align themselves as 'up' or 'down' in magnetic domains. Where it fails is in individual atoms, as in Stern-Gerlach experiments. The famous 'fat lips' postcard shows the actual data and the distribution of up and down spins. They are not +1 and -1. Nevertheless John Bell's first equation insists that they must be +1 or -1. Then he shows that this can't yield the desired correlation and so we get entanglement. I have derived exactly the correct correlation using "classical" spins in an inhomogeneous magnetic field - with absolutely no need for entanglement.
So, just as you say "heads and tails" are an abstraction, spin up and spin down are abstractions, and it is only by insisting that this 'qubit' abstraction is real that we end up with the non-local non-logic of entanglement, which has probably poisoned physics worse than any other abstraction.
Therefore I don't disagree with you that the basic logical abstractions may be wrong, but I do believe the problem is primarily that physicists project inappropriate math structure onto physical reality with metaphysical consequences. Similar analysis applies to the structure imposed on the Dirac equation, and on other icons of physics.
There is so much in your essay that I will need a few more readings of it.
Congratulations once again on thinking outside the box. I wish you well in this contest.
Edwin Eugene Klingman