Dear Jonathan (part 1),
I very much enjoyed reading your essay, which is one of the best in the whole set. I would like to provide some feedback based on Quantum Field Mechanics (QFM) - see my essay, which confirms many of your thoughts and provides refinements with respect to statement made by the people you quoted. More details of QFM can be found in my essay (which took a number of artificial postulating shortcuts to limit content - I'm working on a much expanded version with full background included instead of relying on references), extra notes on the page where you can find my essay, and in a slide deck on my website.
Please don't consider my large volume of comments as critique, because that's definitely not my intention.
Page 1: I fully agree with your statement that a broader framework is needed to reconcile Relativity and Quantum Theory, instead of Quantum Gravity Theory.
Page 2: "many physicists treat equations as though they are facts". I fully agree and, in addition, I maintain that theory should follow from reality (nature) and not the other way around.
Page 2: "it may be more fruitful to acknowledge that there are fundamental incompatibilities in how these two theories are framed, and to find the connecting pieces". It is more subtle than that. I agree with the framing part, but you are almost suggesting to use a reductionist approach to fill in gaps. According to QFM, a holistic approach is needed where all four fundamental interactions need to be considered together in order to describe nature coherently.
Page 2: "it may be more fruitful to work at it through a stepwise approach, as with Electroweak theory being a tangible step toward a GUT, and then proceed to ultimate unification only once we have discovered and explicated additional fundamental unities." The stepwise approach suggests again that we can construct a unified theory by adding pieces to it. According to QFM this does not lead to a unified theory, since a holistic approach is required which considers all interactions together.
Page 3: "This manifests in the form of pairs of virtual particles which appear to pervade space." Virtual particles are theoretical constructs and have never been observed. It is very shaky to use them to construct a unified theory of physics.
Page 3/4: On page 3 you suggest "My new approach involves pairing up other quantities, and likewise asserting that they are two faces of the same thing." and on page 4 "This continues for each combination uniting two of the four quantities - matter, energy, space, and time. Each unifying concept is made more meaningful when considered in relation to the others. So to matter-energy (or mass-energy) and space-time, we can add matter-space, matter-time, space-energy, and energy-time - making six fundamental unities, identities, or pillars in all." Mass and energy are in fact equivalent.
I think you are very close to the correct set of quantities. According to QFM (see eq (2.2) in my essay), the unified relation between quantities is the quantum condition -h = -E dt pdx, where h is Planck's constant, dt is discrete time, and dx is displacement of the massive particle over dt. In fact, dt corresponds to the average of the random internal motion of a massive particle. (see also David Bohm's book: Wholeness and the Implicate Order, page 101, where he states a similar expression, but with a different interpretation of dt and dx).
Page 5: "once we admit the possibility that a broader framework is what's needed to create a more nearly encompassing understanding." Yes, QFM takes a holistic approach for the four fundamental interactions as the broader framework. This framework is mathematically represented in terms of state equation (2.1) in my essay.
Page 5: Time is indeed not an illusionary property of nature and I strongly concur with you on that. In fact, time is an essential element of a unified theory of physics. You can already see that from the stated quantum condition.
Page 5: "space emerges as a manifestation of the extended nature of time" and "The gist here is that time may be more primal than space, energy, or matter, being a sort of prerequisite - a precursor or antecedent - to the existence of these quantities." In QFM, space and time dynamically emerge together, without space there is no time and v.v. Time is not a background parameter.
Page 5: "one can assert that the existence of energy and the laws of electrodynamics proceed from geometry and the properties of space or spacetime". The laws of electromagnetism/Maxwell's equation follows from considerations involving quantum condition -h = -E dt pdx, see my essay and reports on my website for the complete derivation. No "monogenic functions in 5-d spacetime" (purely theoretical constructs) are needed.