Check Navtours. Like the Moorings, their boats are based in Nassau (in their case, at Palm Cay Marina). That's the way to get to the Exumas. In the past, for an extra fee you could drop-off/pick-up at Staniel Cay and Emerald Bay in the Exumas, but I don't know if that's the case anymore. While it saves time, it makes it significantly more expensive. Nassau has the benefit of offering better provisioning and many more flight options. In your planning, just know that you'll spend the better part of your first day getting to the Exumas, and your last day getting back to Nassau.
As far as I'm concerned, the Exumas are worth every bit of effort. But you have to like seclusion and self-sufficiency. You will be anchoring almost all of the time (no moorings, minimal marinas), and there are few places to provision or obtain water/ice.
Let me know if you want more info.
