I have to wonder about the cost/benefit equation. It depends on how you value a largely sleepless night and exhaustion the first day of your stay on beautiful St. John.
How does the cost of a red-eye Jet blue ticket to SJU, a connecting flight to STT, and some sort of solution for the SJU layover compare to taking an earlier flight with a quick connection or a flight directly to STT that would facilitate a good night's sleep and a more energized start to your stay on St. John?