I quite enjoy eating rabbit and it is very easy to get around here. As long as you tell yourself that its really no different than cooking chicken, you should be able to prepare it. The rabbits come skinned and gutted and headless so it really doesn't look like a buuny.
I did a search and found a company in Vermont that will ship to New York. Maybe you could try a month's worth and see if it makes a difference. You could cook the lot and freeze it in meal-size portions.
http://www.vermontqualityrabbits.com/shipping.html
I'm so sorry about poor Chewy's itchniess. Has an allergy medication been prescribed to help control the itching and let the medication heal the staph infection? There must be an oatmeal bath or lotion safe for use on dogs.
Hang in there!