I have kept the boat there for a decade now and I register them both in florida even though the big boat is documented. I do it just to appease them.
My boat is old (1975) and I was able to register it easily as an antique watercraft for under 10 bucks for 3 years at a time. The dinghy costs more, but not much more.
just wait until you are there, if you are documented.
rich