Tobin's right, you'll run into problems with spin. A photon has a spin of 1, so there's no way to conserve spin in an interaction that starts with one photon and one electron and ends up with two photons and one electron.

Sylas, nice work. Lyndon, for all your criticism of Sylas's back of the envelope calculation, you seem to have missed an important point. In every case where he made a rough estimate, he gave your model the benefit of the doubt, and estimated in the direction that would make it most likely to come out physically acceptable. In some cases, he did so by a few orders of magnitude (such as assuming that all of the interacting particles in the plasma were electrons). And your idea still fails conservation of energy and momentum by several orders of magnitude more. So if it doesn't come close to working with the most generous estimates that are reasonable, it can't work if you put in better estimates (which will be less generous).

And do you really still think it's meaningful to compare H and hr/m directly, even though they do not have the same dimensions?