By AWT every artifact with positive curvature should have a positive (i.e. nonezero) rest mass and the photon - being an isolated particle - is no exception. The particle like character of photons can be observed easily during spreading of gamma rays in spark chamber or by scintillator in spinthariscope, where they're behaving like distinst well defined particles ("scintilla" means "spark" in Greek). Therefore it's nothing strange, if photon increases mass of resonator, whenever it gets trapped into it - as we can observe by mass spectrometer during excitation of atom nuclei, for example.
The theoretical rest mass of photon can be extrapolated as a dynamic mass of photon, when the (wavelength of) photon becomes so large, it will fit the whole observable Universe, so that the photon cannot move and it stay at rest in it. This value is incredibly low, though and it can be estimated by using of E=hν formula to some 10E-61 kg. Albeit low, it can result into observable violation of Compton law at Planck scale (pair formation) and into light speed invariance violation at cosmic scale (for example by polarization of microwaves by vacuum and by dispersion of gamma rays, as observed by GZK limit or by MAGIC telescope during Mkn 501 flash).
The effective rest mass of photon could become even higher (~10E-17 kg), if we consider, the photons, whose wavelength is longer then human scale would dissapear in the noise of cosmic microwave backround (CMB) radiation, where only entangled light waves can spread effectivelly. In adition, photons of wavelength larger the human / CMB scale (~1.7 cm) are behaving rather like weak holes in the ocean of CMB photons, so they should be expelled by them in gravity field, instead.
The general problem in misunderstanding of special relativity consist in mixing of light and photon concepts. Light wave can be local, but the photon isn't never quite local thing, it has a finite (albeit typically quite small) size. It means, only light wave can move by speed of light, but not photon. For wavelength comparable to CMB radiation the light can consist only from waves, but not photons, because these size of photons are comparable to CMB noise size, so they cannot be distinguished from it. For longer wavelengths, then those of CMB the negative rest mass photons can be postulated, and the speed of such "negative curvature" photons becomes superluminal - the character of such waves will converge to longitudinal gravitational waves, which are inherently superluminal. The superluminal portion of microwave light enables to escape it from black hole as a Hawking radiation for example, which makes the whole concept testable.
"All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it,
but he is mistaken." (Albert Einstein, 1954)