At c/H, in both the old and new law, the frequency of the photon reaches 0.

But "at c/H" the photons never reach us because their source is receding from us at the speed of light. We never see zero-frequency photons. We do see substantially-lowered-frequency photons (once the light has had long enough to reach us despite the recession).

In the old law, it remains to encounter ever increasing space, getting farther from the things in front of it.

This doesn't appear to me to be anything like correct. It is getting closer to the things in front of it -- apart from ones that are receding from it faster than the speed of light, which are (and remain) far away from it. What's the problem here supposed to be?

Old = photons piling up in ever increasing space

I repeat: I do not think the conventional theory does say anything like "photons piling up in ever increasing space". Of course it's possible that my analysis is wrong; feel free to show me why.