17 chickens in 96 square feet is 5.7 square feet each in the coop. An 8 x 20 run is 160 square feet which gives just under 10 square feet per chicken. There is nothing really magic about the regular 4 and 10 square feet numbers, but they are a decent place to start. I think you have sufficient room for the number of chickens. I would not crowd it much more though. You are probably getting close to your limit.
I once had three adolescent roosters with 15 hens and pullets and never had a problem with bareback. They did free range though, which could make a difference. And different chickens have different personalities. Getting rid of the two roosters will be a positive step, in my opinion, but I don't think it will solve your problem.
Mites and lice could be a big part of your problem. They may be picking themselves because of the parasites. There are different ways to treat the lice and mites. One way is to take the Sevin or whatever powder you use, if you use powder, put it in a garbage bag, put the chicken in the garbage bag up to the neck, and shake and turn the bag to get powder all over the chicken, turning more than shaking since you don't want to break its neck. I'd lock them in the coop to catch them and treat them in the run where you have better ventilation. Some people take them off the roosts at night where they are easier to catch.
I've used the aprons and they soon get used to them. The only problem I've had is that some of the snaps don't hold real well. Two worked great but the third just would not stay snapped. But don't worry about the chickens not liking them or picking them off. That is not a problem.