my policy suggestion is to pay good teachers much more to mentor peers, not for high scores
The "problem" with this suggestion is that I don't think you actually need to pay teachers more to mentor peers. That is, you obviously have to give them time during the day, and pay them reasonably for additional out of school obligations, but overall mentoring, having student teachers, etc. is a reward in itself. I'm not saying it is easy, but then again, neither is teaching kids.
If you want to give them a perk, they'd probably be excited use the college's library and gym for free for the semester.