Maybe this could be combined with the civilian review board idea, and that board (perhaps it could work like jury dutypeople rotate in and out each year or something) chooses from the competing firms...
Seems like outfitting all police with cameras would be a lot easier and more effective.

people rotate in and out each year or something) chooses from the competing firms...

No, it doesn't, at least not in any significant way. What I described has already begun, there are already numerous incidents and the use of body cams isn't even that widespread yet 



