When would you have to return to the Berkshires? Distance and timing may be the greatest decider in where you could leave your boat.
Having just come from several months in the Florida Keys, I wouldn't suggest that anyone store their boat for hurricane season there, though lots of people do so. We stayed at one marina, Mangrove Marina, in Tavernier, where I believe that the staff is conscientious and competent, so if push came to shove, that could be an option. I don't think, though, that their travel lift could haul the average sailing catamaran. There are lots of marinas in Florida, though most insurance increases the deductible for damage that occurs due to a named storm during hurricane season. But you could check out Georgia or states north, better from an insurance standpoint.
Personally, I would want my boat hauled and carefully blocked if I were going to leave it unattended in a hurricane zone. I would also want to oversee the haulout and securing process before I left the boat.
The Caribbean is also a problem area. Though on an individual island basis, a major damaging hurricane hits on average about once every 8 to 10 years, that's not good enough when it's your boat that needs securing, and tropical storms can also do a lot of damage to an unattended boat. I don't have a very high opinion of the employees charged with securing the boats - I've spent 'way too much time down there. About the only reasonably secure places are Trinidad and Venezuela, but both have their problems. Venezuela remains politically unstable with the US being seen as a "bad guy". Though the average Venezuelan doesn't listen too carefully to their politicians, that attitude does color their behavior. Trinidad has always had a crime problem, it's just being publicized a lot more recently, and theft of yacht gear is apparently more prevalent now, perhaps because there are so many US boats left there for the cyclone season unattended.
St. Martin has become a very popular place with what seems to be about a dozen marinas built in the last 10 years or so. Theft has always been a problem in SXM - so many tourists. But a better chance of getting hauled.
There are many boats who spend the winter season in the Caribbean and the summer in the US. Since you know you're going to have to leave the boat, you would be advised to check each stop on your southbound journey to check out places you could safely leave the boat, and think about how long it would take for you to get back there in the Spring.