Hey Chico,
in my opinion I think you should not allow your bird on your shoulder, considering he is being very possesive. I allow tango to hang off my shirt, cuddle inside my shirt and crawl all over my chest, but when he trys to go past my shoulders I stop him. He's never allowed on my shoulders because I had the exact same problem as you. Now when he gets on my shoulder by accident I find it very easy to take him off because he already knows he shouldn't be there. He doesn't bite anymore, so that means no more missing chunks of skin.
This is my opinion, and I know everyone has their own. You don't have to listen, it's just my advise.
Creds: Certified Professional Dog Trainer