Hi Jason
J; "Do you think your inertial frames and the Higgs field have anything in common?"
Certainly, but only in that there is certainly a field in space. I see no evidence for the Higgs particle, indeed au contraire, and am confident it won't be found. 'c' can only ever be 'c' wrt a local field.
J; "Second question: do you think that Higgs field compression/shock waves might explain
(a) Inflation theory (the first few superluminal microseconds of the universe) and
(b) the M87 superluminal jet that was belched out at 6c?"
Much more precision would be needed for a precise answer. We can be very dim. Inflation theory can only work with a field, and therefore waves. If it's only a vacuum that inflates there is no inflation, there are only unconnected bits of mass. Yet we know each bit of, or grouping of bits of, mass has it's own complex fields. Even our galaxy has, so is, an EM field. The field/s will obviously expand into any vacuum around it/them and 'thin out', affecting it's properties. i.e. permitivity, which, contrary to Maxwells basic equations, we know varies with frequency. We also know each local magnetic field for instance has limits and therefore boundaries, and there are infinitly many, relating to all parent mass and to relative motion.
M87 is merely a superposition of feilds in motion within each other. The inner one does 6c wrt us, the observer. None do more than 'c' locally. It's almost too simple.!
I can indeed perceive the universe as the biggest 'Shrodinger sphere' wave, within which infinitely many others move, wax and wane. I quite like your 'big froth of wave functions', but think you need to modify your 'frequency shift photons' to make them fly in the real world.
Consider apparent frequency and wavelength between moving frames a bit more Photon wavelength is shifted by relative motion - i.e. when changing inertial fields (i.e. from the suns to the earths) the photons hit the first electrons moving with the new field, are absorbed, then re-emitted at the NEW local 'c', which gives them a different frequency if the observer also moves into the new frame, or wavelength if viewed from either 'other' frame, from where apparent frequncy is conserved. (the Doppler shift cancels out the motion).
You may need a brain the size of a small moon to first work that out, but once you've absobed it you'll see how simple it is.
(The 'Classic' version of all that works the same, as Huygens principle and the Ewald-Oseen Extinction theorum).
But it's crucial you allow yourself to 'test' the model of photons as duel phenomena, only locally propagated/condensed as 'particles' and reforming as wave energy until next perturbated for the next frame change.
I appreciate your trying to escape the box but am not conviced you'll make it as we all have to resort to touchstones and old concepts when overstretching our brainpower outside preconception, but please do try. I wish you luck.
Peter