Dear Israel,
Your enjoyable essay makes a very good case for more ontological reasoning in physics, rather than just remaining lost in the maths wilderness, where we have been stuck for decades in many areas of physics.
My particular areas of interest are particle physics, time and the aether. By complete chance, back in 2002, I discovered a new preon theory, which I have named gimli theory. You quote Feynman "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." Gimli theory works and gives consistent outcomes that agree with experiment.
The point here is that a reductionist theory that works (agrees with experiments) can give new structural insights into the world of particles, and these insights can lead to a dismantling of much of the patchwork of quantum field theories of the Standard Model. Gimli theory is not based on heavy mathematics at all, yet it can provide many answers to big questions because of its ontology.
My grumble is that mainstream physics journals do not want any "maverick" theories challenging the status quo, unless put forward by a Nobel laureate, and even then it may still be difficult. New physics theories heavy in math tend to be only read by the few in the clique, and are often beyond the grasp of philosophers of physics.
You state that physical understanding is crucial to make headway; otherwise we might continue to be lost in math and measurements. I fully agree with you!
As my entry is my first ever FQXI essay, I tried to stick to examples of undecidability, computability and unpredictability, in my considerations of a TOE, although I do wander on to the philosophical time topic of presentism which I currently endorse.
I am currently reading your 2012 FQXI essay "The preferred system of Reference Reloaded" which is a brilliant essay. It is a pity that I have only just discovered FQXI, partially due to me working in almost total (physics) isolation for the last twenty years developing my 'structural' theories of space, time, aether and particles. The advantages of being a hermit (not visiting physics forums) is that you can keep ideas pure during development. Of course, one needs good reference material to work with from the start.
Good luck with your essay and 'may physical theoretical frameworks come into prominence'! (ie. may the force be with you)
Lockie Cresswell