You might look into S.water Caye. It's in the Tobacco region just south of Tobacco Caye. You won't have the dozen acre island to yourself (there are 3 resorts on it and every inch of the island is owned) but its pretty isolated and quite. I contacted International Zoololical Expeditions, (IZE) and negotiated a very resonable price for transportation to and from the island, meals and a place to ptich a tent. IZE mostly caters to college students doing marine biology studies.
Meals are served dorm style at set times, they have daily and nightly dives, its close to glovers atoll, they have sea kayaks and other water equipment.
IZE worked out great for me, as long as I was willing to work around their schedule and be flexible. So great infact, that if I can't figure out something for turneffe or lighthouse I will probabaly go back.
As for camping on Lighthouse reef, camping is allowed on halfmoon cay. Their is a park ranger and their is a day fee. I am also, trying to find out about camping on sandbore cay. From what I've read there is a lighthouse keeper on the island and it's located on the reef.
For turneffe, just yesteday I e-mailed three of the resorts on Turneffe and inquired about camping on their ground or nearby islands. As these are evepensive, exclusive resorts,I don't expect too much to come from this this but it's worth a try.
When are you going? Have you inquired with the overnight dive boats that go out for a dive and then sleep on the boat or camp on one of the islands? If we end up going to belize at the same time are you into spliting the cost of charting a boat to one of the outer islands?
Hope this has been helpful,