I wouldn't get too excited

This is correct I shouldn't. I saw words and symbols that I would use in a way I would use them. I keep forgetting all of those words have different meanings to you and others. For instance the word time means something different to many than to myself.

The proper energy of the photon E is a function of the emission energy Eo.

We have different ideas of emission energy's foundation. Your perspective is the electron as the source of propagation of the photon. Equivalence between SR and GR would suggest differently.

The resulting equation is E = E0/gamma. This is independent of time.

Here is where we have a different understanding of time. Planks distance is a time segment. Eo in space far away from mass has a planks length for the time segment. E0 is the planks length in the highest dilation of space energy. So there is more density of energy in space than in dilated space. There is a different distance length for dilation in GR relative to how we measure time. So Gamma (dilation) is not independent of time energy distance.

An equation for tardyons may depend on time.

Of course, which is the gamma term in Relativity.

Gamma in the above relates to the velocity of an SR inertial frame of reference through which the light passes. This does NOT apply to GR.

Geometry is the equivalence between SR and GR. GR is physical and SR is visual equivalence. I can show the simple equations for SR length vs. time measured in SR. If you follow light being independent of the source a Relativity postulate. Momentum is not a factor in light speed.

This does NOT apply to GR

It does as equivalence. All measurements are done in GR.