Idea - what if instead of a single screen depth map, we created a cubic one into a cube map, then used THIS to calculate the screen space reflections. Wouldn't this work better? Or am I over-looking something?

Probably the idea everybody had, but nobody ever tried :D

It would work better for sure, but still lacks occluded information. So it's questionable if rendering 6 images instead just one is worth it, even if the others are at lower resolution.
But eventually update only one low res cube face per frame, and reproject to compensate?

BTW, it would not work well to calculate specular for stuff behind the eye, so doing just diffuse term would be another optimization.