You mentioned "Physics realism: physics is the territory and maths is the map
Maths realism: maths provides the territory and physics is a map"
Thats true and its is because there are existing laws of invariance which governs both mathematical structures and physical reality. Its not mathematics describing physics rather their respective laws of invariance match each other.
In context of Skolem paradox, that's the reason why sometimes athematics and physics describe each other sometimes right(when they match) and other times wrong(when they don't match)."A particular model fails to accurately capture every feature of the reality of which it is a model. A mathematical model of a physical theory, for instance, may contain only real numbers and sets of real numbers, even though the theory itself concerns, say, subatomic particles and regions of space-time. Similarly, a tabletop model of the solar system will get some things right about the solar system while getting other things quite wrong."
Mathematical Structure Hypothesis by me which states that Mathematical Structures and Physical Reality both originate from Vibration and that makes it possible for one to describe the other. Thats why Godel's Incompleteness theory indicates towards the fact that "In any axiomatic system of mathematical structure, there definitely will remain at least one statement(e.g. concerning self reference),where there will be required intervention from physical realities." And thats why we see that physical theories e.g. string and other theories are used to crack toughest riddle in number theory and other disciplines of mathematics. Riemann Hypothesis is a vibrant case. And vice versa from physics to mathematics(no-go-theorems) which you have classified in two categories of realism.
If we combine Skolem with Godel what can come out that "Inconsistency/Incompleteness in one frame/world can be made consistent in other frame/world." Godel Incompleteness and axiomatic paradoxes basically reveal that though mathematical structures and physical reality having same origin why we allow time and frame of reference in physical reality but not in mathematics. This limitation leads to such conflicts.(which I have explained in my essay). I want to lead mathematics to evolve and expand in that direction.
As far as you referred to Bell's theorem and EPR paradox about the no-go theorem in physics, let me quote references from my essay by David Bohm, former associate of Albert Einstein
"The interrelation of human consciousness and the observed world is obvious in Bell's Theorem. Human consciousness and the physical world cannot be regarded as distinct, separate entities. What we call physical reality, the external world, is shaped - to some extent - by human thought. The lesson is clear; we cannot separate our own existence from that of the world outside. We are intimately associated not only with the earth we inhabit, but with the farthest reaches of the cosmos."
Entire Universe exists within an atom and the same atom exists within the Universe. David Bohm maintains that the information of the entire universe is contained in each of its parts. This is because of Vibrational origin of External clasical world, which is fundamentally Quantum effect only .(I have tried to explain in my essay). This peculiar geometry leads to Bell's locality -at-distance and EPR paradox. This is related to geometry beyond Russell's paradox . It is possible that A is a subset of B and B is the subset of A in different reference frame and time . But constraints in mathematics in the dimension of time and reference frames leads to contradictions, paradoxes.
This is what Swami Vivekananda who hinted at relativity theory decade before Albert Einstein and great scientist like Nicholas Tesla, Bose used to take guidance from him.
'Time, space, and causation are like the glass through which the Absolute is seen. ... In the Absolute there is neither time, space, nor causation.' -Swami Vivekananda.
The modern science which binds witself within the periphery of TIme,Space, Causation is trapped in the Bell's locality-at-distance andEPR paradox in Quantum Physics.
Nic Herbert, a physicist who heads the C-Life Institute, suggests that we have merely discovered an elemental oneness of the world. This oneness cannot be diminished by spatial separation. An invisible wholeness unites the objects that are given birth in the universe, and it is this wholeness that we have stumbled into through modern experimental methods. Herbert alludes to the words of the poet Charles Williams: "Separation without separateness, reality without rift."
It would be a mistake to suppose that these effects operate only with relevance to the invisible world of the atom. Professor Henry Stapp states that the real importance of these findings is that they translate directly to our microcosmic existence, implying that the oneness that is implicit in Bell's Theorem envelopes human beings and atoms alike.
The interrelation of human consciousness and the observed world is obvious in Bell's Theorem. Human consciousness and the physical world cannot be regarded as distinct, separate entities. What we call physical reality, the external world, is shaped - to some extent - by human thought. The lesson is clear; we cannot separate our own existence from that of the world outside. We are intimately associated not only with the earth we inhabit, but with the farthest reaches of the cosmos.
I have mentioned these things through references
Anyway your essay is great.