If one has mites or lice they all do. You need to treat them all.
That sure looks like damage from mating, but I'm not ready to call it over-mating. I suspect it's from the two cockerels you just removed. Hens often don't squat for cockerels so the cockerels get physical. That kind of damage is not that unusual when you deal with cockerels. I'm not sure what kind of interaction was going on down there. Usually an older rooster will stop the cockerels from doing that. Usually if a cockerel starts bothering her my hen runs to a mature rooster and let him handle it. I'm assuming this damage is new.
Another thought is bad technique. It's possible one of your mature roosters is causing that problem because he doesn't know what he is doing. Quite possibly the hen does not respect him enough so he has to force her. Usually that the rooster at the bottom of the rooster hierarchy. The hens usually prefer the stronger ones. If you can, observe them and try to determine which one it might be. That way you don't just kill a random rooster and not stop the problem.
I'm not sure what your goals are or why you want three roosters. I generally suggest you keep as few roosters as you can and still meet your goals. That's not because you are guaranteed problems with more roosters, just that problems are more likely. I'm not one to believe in that 10 to 1 hen to rooster ratio or civilization as we know it will forever change, I've seen too much evidence that disproves that. I've had three roosters with fifteen hens without damage like that. One member on here free ranges a lot of flocks, basically lets them sort it out naturally. His average flock size is one rooster and seven hens.
This damage is unlikely to heal until she molts, though it might. If a small part of the feather is left behind, she will not grow a new feather until she molts. If the entire shaft is gone she should regrow the feathers soon. If the damage gets worse now that the cockerels are gone I'd look really hard at those three roosters.
