Well a muzzle won't help with calming, it is strictly for protection of others.
My vet actually works around Korbel's psycoticness. When Korbel hisses, she checks her teeth, stuff like that.
What has helped with Korbel is that they've given up on keeping her in a cage. They set aside an exam room if Korbel needs to stay for any reason. They just set her up in there with a litter box and the staff can go in and check on her. Korbel does much better that way, but she has extreme cage aggression, so I'm not sure how that would work in your situation.
As for muzzles, I've never tried one on her but I know they make them. If you're concerned about Quinn biting someone it would be worth looking into. Also, I've heard of people using a light sedative on aggressive cats before taking them into the vet. THat might be another option to ask about.