Marc . . .
Thank you for a very excellent and easy-to-read essay. Your explanations were clear and reasonable. I have been thinking along very similar lines.
I especially like your ISAAC (Infinite Set of All Abstract Computations), although I would leave out the Computations and see it as IDAA, the Infinite Domain of All Abstractions. This is because I don't see why everything has to be a computation. (Not as keen an acronym I will admit. I'm a fan of Asimov!)
I do believe that mathematical structures can form the physical universe, but there is no need to try and force intentionality out of computations. Mathematical structures are a subset of a greater abstract entity, one which includes all other non-computational structures. This abstract entity I would call the Ideaverse, which is the infinite domain of all Ideas, or Abstractions. Human qualities such as awareness, intentionality and other attributes of a mind, such as desire, imagination, curiosity, goal-seeking and love, that seem to be difficult to obtain from mathematical laws are still ideas, just as mathematical structures are. So just as mathematical ideas are the physical universe, abstract ideas like intentionality are intentionality.
You brought up the HPL, Hard Problem of Lawfulness. "If every possibility exists within the Maxiverse, irregular and chaotic worlds should greatly outnumber regular and predictable worlds like ours." One explanation is that the "Maxiverse" (or Ideaverse, as I called it) is an abstract reality. It does not have existence in the sense of being perceivable, so those chaotic worlds remain only abstractions.
But within the Ideaverse is the idea of Mind, which is the idea of an activating agent of ideas. Mind is that which activates ideas, including mathematical ideas, and makes them existent and perceptible. This is equivalent to the opposite of abstract, that is to say, "concrete." So the mind is what activates ideas that are reasonable and at least somewhat stable. This includes the ideas of a physical spacetime universe, intentionality and goals.
You say, "In the same way, could the dead-ends we have been encountering over the past decades in fundamental physics (the failure to unify quantum mechanics and general relativity, the proliferation of solutions in the landscape of M-theory) be interpreted as signs that we are nearing the edge of our patch of lawfulness in the space of all possibilities?"
Interesting, as this is the interpretation I made in my essay. Not all ideas the mind activates will mesh with other ideas that it's already accepted.
Thank you for the great references you gave, which will serve me well in my further study and contemplation.
Michael Z. Tyree