Jason,
It could be that, as you say: "when the two slit experiment is performed, one particle (electron or photon) at a time, the particles still form a diffraction pattern. That tells me that the wave-function(s)permeate the whole experiment."
Or it could be that each particle is accompanied by a 'pilot wave' as deBroglie, Schrodinger, Einstein, and others insisted, at one time or another, and that this 'local pilot wave' aspect of each particle accounts for the 'particle by particle' creation of a diffraction pattern. If each particle did *not* have an accompanying 'wave' aspect, we would be hard put to explain how the sequential sum yields an interference pattern.
Therefore, if photons and particles are discrete, and can be identified by a mass or a frequency, they must be accompanied by an aspect of reality that exhibits wave-like properties on a particle by particle basis. Only the C-field provides this physical 'pilot wave' that experiment seems to demand.
As for 'wave-functions' permeating an experiment that is performed over hundreds of kilometers it depends. If by 'wave-function' you mean a mathematical description of the experiment, OK. But if you mean a "physical" field or phenomena, based on two particles from a common source and extending for kilometers (or light years) then I can't buy that.
But it's not needed. The local pilot wave is 'attached' to the local particle in the sense that the particle momentum induces the C-field (pilot wave) circulation analogous to a charged particle inducing magnetic field circulation.
This 'local reference frame' fits with Peter's ideas and Einstein's ideas as quoted in Peter's essay. It also explains the constant speed of light in local reference frames and answers your earlier question about information being lost when a photon is red-shifted.
I haven't tried to solve the Casimir effect in terms of the C-field, so I have no opinion there, but you're right, the next question is how wave functions 'push'.
The Lamb shift is more interesting. I suspect that it is a C-field effect, but I haven't shown it. First, I think it is the right order of magnitude to be a C-field effect. And I don't really believe it's a 'virtual particle' effect for two reasons. Relatively recent QCD experiments expected to see a 'sea of strange quarks' in the proton, and have not found them. But even more serious to me is that the vacuum energy is now known to be 120 orders of magnitude weaker than was believed when the Lamb shift was calculated, but this factor of 10^120 does not seem to have any effect on the calculation of the effect. How can this be? When your primary explanation undergoes a change of 120 orders of magnitude in your primary variable, vacuum energy, and has no effect, perhaps it's time to re-examine your explanation.
Finally, in the GEM and the Constant Speed of Light paper, I have ignored the term that is based on changes in gravity. I plan to go back and look at that (real soon now) and will be happy to discuss photons and gravity with you at that time.
Edwin Eugene Klingman