re: Any different islands I should check out?

Don't have time to write much, but I've been to most of those islands on your list and Exuma has everything you're looking for and more. It's an incredible island - Coco Plum Beach at low tide is the best I've ever been to and you won't see hardly a soul at the beaches. It's crazy. Very uncommercialized and great people. Very safe. We rented a house in February Point and it surpassed expectations.