>So how do you prevent schools either going into a vicious or virtuous cycle?

I expect that you have to try it and add controls as necessary. Not only are these systems too complicated to model in any simple way, but have multiple players each with their own demands. It's a strategy problem as much as simply channeling some money.

It seems to me that the end game always becomes one of segregation of 'good' vs. 'bad' students. The teaching part isn't purely an aside, but matters less than you might think. So, you have to ask how important it is for the good to drag along the bad (or visa versa) and how detrimental it is to produce schools that are, in essence, jails.