@joeclark reading your post I see two possible problems right off the bat with your living on the boat - being confined with your dogs in a small space (considering dander is one of your problems) and vestibular problems (possibly being caused - or exacerbated - by the constant swaying in your boat).

My daughter has severe anaphylactic allergies to everything including your list (minus dogs, cats and peanuts .., yeah, go figure!) and she finally was put on monthly Xolair injections which are helping a lot. Perhaps you could ask some doctor to prescribe that for you …? But again, being “Stateless” you might have a problem getting a prescription for it, because Xolair has to be administered in a clinic or hospital.

Could you ask to be put on a waiting list for a cancellation, so you can get an earlier appointment date with the University of Michigan?

This link, provided by @johnbishop is worth looking into - but I do feel the dogs and living on the boat are compounding your existing problems. In fact, living with dogs may be the underlying problem …? Just my two cents’ worth. 🤷🏼‍♀️

U.S. State of Residency while cruising: https://forums.sailboatowners.com/threads/u-s-state-of-residency-while-cruising.138278/