You have impressive detail about a diverse number of sometimes quite complex notions. Yes...matter action is the only way that I can explain the observations of science and also unite quantum gravity with quantum charge. It bothers me that no one else seems to be able to unite gravity and charge since matter action does it so well.
I hope this will be useful to you and I do encourage your further endeavors. Matter action does explain the nature of physical reality but I really cannot claim to have the only solution to the universe and matter action may indeed have some fatal flaw that is not yet apparent. After all, there are lots more people smarter than I am out there so why should I be the only one with unification?
The notion of a wavefunction is simply an expression of the quantum nature of matter. All matter oscillates and when matter oscillates in phase, it can bond. The phase coherence of matter oscillation can persist even with separation and that is entanglement. Exchange of light photons is how matter bonds and so light exchange is the glue of both charge and gravity.
You bring up the notion of the universe as a wavefunction, with which I agree. In fact, the universe wavefunction is how matter action quantum gravity relativity works. There is no way to measure and therefore know anything outside of the universe. In fact, just as you point out, there are even many things even within the quantum universe, i.e. mysteries, that we cannot measure and therefore cannot know as well. Quantum entanglement is at the root of things that we cannot know and yet entanglement does affect our lives and so you are right in your surmise about entanglement.
The multiverse and multidimensional stringy and loopy notions are all interesting religious beliefs just like reality as a simulation by some master simulator. Since there are no measurements that affirm or deny these religions, I prefer to avoid them. My preference is to keep things that science measures separate from religious beliefs about the mysteries that do exist. Philosophical discourse is about questions and mysteries that really have no unique answers and yet there are many questions that may in fact have answers that we just do not yet know. Therefore philosophy does provide a useful discourse distinct from the measurements of science the beliefs of religion.
Inflationary bubble universes emerge from the notion of inflation, which is a patch to the make big-bang universe singularity consistent with the uniformity of the CMB. Since matter action is already consistent with the uniformity of the CMB, matter action does not have any singularities like the the big bang or the patches like inflation.
The fundamental notion of a singularities in spacetime is what spins many narratives and also spoils many notions of unification. Since matter action is made of discrete particles, there are no singularities since space and time both emerge from discrete matter action. Black holes are singularities in spacetime but black holes are just pure phase in matter action. Black holes are the ultimate destiny of the matter action universe and not really a singularity.
Matter action supposes that the universe is made up of a very large but finite number of aether particles. Matter, space, time, and motion then all emerge from the actions of those particles, what we call change.
Boy, you bring up quite a cornucopia of notions. The notion of finetuning makes no sense in matter action since matter action is a cycle of universes where many constants vary together, not individually. There are just two constants for each universe cycle: aether particle mass and action constant, i.e., Planck's constant. All of the other constants derive from just these two along with the dimensions of matter and action with quantum phase.
The universe collapse is the half cycle outcome that emerges from a half cycle precursor that is an antiverse expansion of antimatter. This is the causal set of precursors and outcomes from which space and time then emerge.
It is true that the Schrödinger equation is based on continuous space and time. However, the Hamiltonian step operators are the discrete basis for quantum electrodynamics (QED), which is actually how things work. Discrete operators form the bases of the Hilbert spaces that you mention, but do not elaborate on. It is important to limit the complexification of things by bringing in too many complex terms. It is better to use as simple language as possible for civilians and save the complex math for the technicals...
You mention four force vectors but this means you are in spacetime. All spacetime forces emerge from particle exchange of quantum field theory and so matter action forces are all exchange forces, not vector forces. Vectors emerge from space and time.
Physics often uses extra dimensions to fill in blanks of knowledge. Matter action has just the two dimensions of matter and action and along with quantum phase, is consistent with measurements. Matter and action are a Hilbert Space, but there is no need in matter action for another 8 to 48 dimensions to unite gravity and charge. All that is necessary to unify gravity with charge is to include the acceleration of light along with the speed of light. Then the bonding of charge is a result of photon exchange and the bonding of gravity is due to biphoton exchange. All matter, after all, is the result of photon exchange bonds with complementary and entangled photon emission. This entangled biphoton exchange is the basis of quantum gravity relativity.
Thanks for mentioning holographic entanglement entropy, HEE. I had not even known that this was a big deal until you mentioned it. Of course, it is quite a complex notion and involves lots of quantum field theories, anti de Sitter spacetime, and so on. These are all notions that might unify gravity and charge in spacetime, but matter action already unifies gravity and charge. So HEE is just a lot of complexity just like stringy and loopy and antiverse and singularity that matter action does not need.