Yes, Antigua is better for a nonpaid position. Hang out at the "Mad Mongoose" in Falmouth harbour both during the day (stick around the outside with the
power strips and free WiFi) or at night in the bar and if you don't make a fool of yourself and don't care which direction you are heading then you'll almost certainly get a slot. Numerous bulletin boards at the Falmouth marina and around
English harbour are scanned by boaters looking for crew as well. Everyone going north or south stops at Antigua. If you can arrange to get there before either the Bucket or Antigua
Race Week your chances are even higher for finding a position during either
race and, if you acquit yourself well there then the grapevine will find you a slot.
I would recommend looking into getting your STCW95 while still in the
USA and with that certificate and being in St. Martin or Antigua might be sufficient to get you hired on for a (badly) paid (deck hand slavery) position.