I switched docs mid treatment, though not in different states but in different cities.
Try to get a referral for a GI or heptologist where you're moving, let them know what you're doing and go for it. I don't see where there should be a problem.
If you're planning to move soon, I'd wait to start tx until after the move.
Good luck, OH
Yes, but it would take some set-up beforehand to pull it off. Treatment requires working fairly closely with a gastroenterologist (preferably one specialised in liver diseases) to monitor how your're responding to the meds and the side effects they cause (temporary problems with the blood).
You would need to line up a doctor in each state to work with. If they aren't on board to begin with, you may have to stop the drugs and wait a few weeks to a month to restart with a new guy in a new place. Stopping and starting the drugs without a medical reason can greatly affect the effectiveness of the treatment and should be avoided.
You could do it but not without pre-arrangement.