I wouldn't choose Exuma. The guides there are total jerks. If you're getting barbeque at Speedy's in flats shirt you'll get accosted by them, never mind if you're in the water. About the only thing you can do is go to airport flat after 5-6pm when they are leaving to run their fatcats back to the Four Seasons.
Acklins is the place for DIY, from the north end to the south end and everything in between. Take a couple of days on Crooked as well. Eleuthera was 'ok' but no Acklins.