Having been at Foxys for this I would consult with your captain but do what George suggests which is what we have done which is go to Little Harbour or Diamond Cay and land taxi over and back...
We really enjoy Diamond Cay for its serenity and if there is a North Swell you walk to the bubbly pool from there. Our 28 and 26 year olds have been going down there for 20 years and for the most part enjoy the time with the other families that go instead of looking for the outside party like NYE or Full Moon...
They will enjoy a day on White Bay JVD with Soggy et.al.
so you may go to Anegada, sail down to Diamond Cay from there (weather permitting) and then go by cab by day to White Bay, reset, and then go to Great harbour for NYE. May want to bring bug spray to Great Harbour
All IMHO
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