Get appointments before you move! Once you have your address at your new house I would call whatever specialists you need in that area to make sure you have an appointment as soon as you can to get set up with care when you get there. Also once you have your first appointments see if you can sign records releases so that your new docs can get the records from the old docs (I am a frequent mover with EDS, POTS, and DID so I feel u on all the doctors)

I don’t know if this will be helpful, but for my move last year, I asked my previous doctors for recommendations of specialists in my new city. That way I knew I would be seeing people who know a lot/enough about my conditions :)