I don't want your cookie. It's probably what caused that "typo."

The reference frames of the photons in your description are not equivalent. They may lack time, and see the universe as a volumeless sheet, but they all see a different sheet. Their FoR's are not equivalent.

E = hf for a photon.
There's no minimum energy, E, nor minimum frequency, f. h is Plank's Constant and describes the proportional relationship between energy and frequency.
There is no quantization of allowed energies aside from the maximum wavelength that could fit in the Universe, stretching from end to end. So long as the universe is finite, that wavelength is non-0. If the universe can reach "infinite" length across it, then there can be photons which are infinite red-shifted... Stretched to non-existence.

It's interesting to speculate a quantum entangled ground state where all photons have been stretched to overlap... that's at least like what you're describing... though from a QM argument and not a GR argument.