Did you have a survey done in the Dominican Republic before buying? Are there other issues or just the bottom needing cleaning and painting. Well, I guesss that's a rather ingenuous remark, all boats have "other issues," it's the nature of the beast.
Since hurricane season runs from June 1 to December 1, you might be better served bringing the boat to Florida for checkout and any work that might need to be done, then heading for the Caribbean after hurricane season is over.
Although we had our boat hauled in Martinique many years ago, I do not consider it the best or most economical place to have work done, and if the yard is no better than 15 years ago, you are going to find the facilities worse than meager. The Euro is so very strong right now that you will pay almost twice as much for work and materials as elsewhere. St. Martin is completely duty-free so at least you can save on imported items, and there are a lot of boat yards there, though nowadays they're all chasing the megayachts. There is a good chandlery, Budget Marine, which is on the Dutch side of the island.
Puerto Rico is often overlooked, but it has much to recommend itself. US, no duty or customs hassles for gear brought from the US. The USVI are a decent place to have work done, there's a large yachting community there.
The major considerations are hurricanes and insurance.