I've resisted posting a reply to your queire just waiting to see what other folks come up with. Around 2006/2007, my buddy and I were in the same boat as you. Being frequent visitors to the island and constantly looking for "out of the way" places to fish...the southern Savannah Sound area was on our list. Fortunately for us, one trip to L'utra while staying at the Duck Inn, we met a couple staying there whom had purchased property there and had plans to build a vacation home exactly where your interests are. The road to their property is private and protected by a chained entrance directly off the Queens Hwy. We received permission from them to use their private road and park on their property for a Bonefishy outing. (We paddled our Sea Eagle inflatable Kayak from there) Google Earth recently updated their images of some portions of Eleuthera and it seems as if our friends dreams have come to fruition. At the end of the most major south Savannah Sound access road...you can see 3 or 4 homes including theirs.
The southern flats of Savannah Sound are expansive and varried in composition. Anything from hard bottomed white sand flats to marly "loon ****" sinky bottoms that'll suck your Simms bonesneakers and socks off in an instant.
If you're looking for more flats like the famous Savannah Sound Schoolhouse flats...there aren't any.
One option for you would be to rent a kayak and drop it in at the public boatramp by the Savannah Sound/Windemere Is. bridge. Paddle north or south dependant on tide and explore to your hearts content. Don't forget, there are plenty of "alternative" species available on such outings that can provide you with a fantastic meal at the end of the day. Work the mangroves for Snappers and Gag/
Black and/or Nassau Groupers that like to hang out there. Lots of large Blue Crabs around too on the grassy flats...1/2 a dozen per person makes for a wonderfull BBQ.