I suspect that most mooring ball operators don't want to hear from you more than 3-4 days in advance. If you call 6 weeks early they will just forget. This is the Bahamas
Beach or Little harbor are good choices. It sort of depends on if you want something to do- like visit Pete's Pub and the art stuff or just lie around and soak up the sun.
Another suggestion would be to head over to Treasure Cay for a night, then Bakers Bay and then back to Marsh Harbor. Treasure Cay is supposed to have one of the top ten beaches in the world.
All of the desitinations you mentioned are within a half day or so sail. Little Harbor is the farthest, but easily doable if you leave early.