I would recommend that you bite the bullet and live wherever you want. The amount of extra
money it will cost you to pay a state sales/use tax is a small
price to pay for having a secure base of operations that is hassle free. Moving a vessel around to avoid
taxes is expensive, time consuming, and inconvenient especially when you have another life. Add on top of that the challenges created by hurricanes and tropical storms limiting your ability to move the yacht at the time you need or want to make a move.
The lifestyle that you are talking about sounds like you will be away from the yacht for significant periods of time. Your highest priority should be a secure location when you are away from the
catamaran. If you are flying around the world and USA a great deal, your second priority should proximity to airports that are convenient and affordable.
Hurricane season happens five months a year, and a location that is safe from hurricanes should also be a high priority. The last priority should be sales/use tax.
That's my two cents.