I don't think putting a saddle on her will draw negative attention from the flock. For one thing it will protect her somewhat from the roosters spurs, and also allow new feathers to come in. Putting a saddle on the alpha hen might be a good idea . If she doesn't like the saddle she will be too preoccupied to cause any feather picking herself. Just don't get RED saddles, chickens are attracted to red. Actually, a nice, blah, boring color would probably fit in best.
and Welcome To BYC!