I have my Caribbean area policy with the brokers, Besso, Ltd, in London. They represent T.L. Dallas (Special Risks). Ltd., and ultimately the underwriters, Great Lakes.
They agreed to allow me to store the boat within the "Box" (Antigua), at a somewhat higher premium than "out of the Box". My total premium is 1.84% of the "agreed value", with a 2% deductible, doubled if damage is from a named storm. Any of the Caribbean islands are OK with them. They charged me less for Grenada, three years ago.
I've had one small claim in three years, and they handled it fairly.