JetBlue,
If you call them directly usually they have rooms. I always called Hotel Aloha Sol directly and never had a problem making a reservation. I can't speak for the hotels, but in my experience being completely booked is not the case. In fact, many of the websites such as Expedia, Travelocity, etc. buy a block of rooms/reservations and sell them. They only put that it is "sold out" because it is sold out on their end not on the hotel's end.
-Jbars