From what I gather, it is essential to fully expose the film/paper in order to "recycle" it. I would think if your HP3 is partially fogged and you develop it, you won't achieve a "max black" before re-halogenization, otherwise the bleach will only act on the grains which are partially oxidized and you'll still have the same problem (only in reverse). In no way would it be possible to bring the film/paper back to its former glory. It is, as PE is quoted beforehand, "reverts[ed] to a simple blue sensitive emulsion with low speed, usually in the ISO 3 - 40 range if you are lucky." which makes sense. Initially, I wasn't sure about the color sensitivity. But now after reading the previous posts and a bit of research it makes sense as well as why it would not retain its original spectral sensitivity.
Not sure about the other bleaches as I have very limited experience with them as I usually use a Blix provided in kits.