You currently can’t fly directly to Anegada as it is not a covid point of entry for customs. What you can do is book a flight SJU-EIS then Anegada. You will clear customs and COVID at EIS and jump back on the aircraft to fly to Anegada. It will be a extra cost.
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The OP is trying to fly out directly. Can you think of any aircraft clearing rules that would prevent this?
Air Margarita is a good option to try. We've use them in a pinch before when we had issues with Air America Caribbean (who was great pre-Irma).