I could envision it being more of an adult themed spot - requiring almost no staff. Just maintain a boardwalk through the island, mount various bird feeders and bird-friendly feed plants to draw more of the local wildlife there, with maybe just one casual restaurant near the dock with restrooms. Purchase a pass to board the boat to get there, enjoy the nature and solitude. For birders and photographers it could make for a nice little side excursion. Boats would leave from the campground dock, sunlight hours only.
All around Florida there are many wetlands and wildlife reserve areas with boardwalks and local wildlife - most are free, some charge a fee to park or get in the gate. Disney even has one (Disney Wilderness Preserve) obviously on a much larger scale. But look at Gatorland nearby - aside from their gator park, just outside they have a popular rookery where local birds nest and roost - they charge to get in but don't need to man it regularly. Merritt Island has a refuge as well as Black Point Drive, Apopka has a drive-through reserve, Viera Wetlands, Ding Darling refuge, and in my part of town, Green Cay Wetlands and Wakodahatchee Wetlands (not too much bigger than Discovery Island).
So many spots throughout Disney World and the resorts already have places where the local wildlife gathers, roosts, and even nests - Animal Kingdom's river area popular with ibises, Epcot's fireworks river popular with anhingas and great egrets, Saratoga Springs with turkeys, nesting great blue herons, bald eagles, anhingas, cormorants, limpkin, and kingfishers, among others.
Right now, Discovery Island is mostly just abandoned - it's not really much in the way of a bird sanctuary or refuge - it's badly overgrown and not just with native plants. While local birds occasionally visit, there's no serious nesting activity there. Clearing out the overgrowth, and replanting native plants only would actually make it MORE of a draw for birds and other wildlife, even with a boardwalk running through it with people walking by. In fact, a lot of Florida birds find proximity to people to be safer for their nests, as it helps reduce egg raiders like raccoons, rats, snakes, and other predators. My local wetlands rookery spot has 500-700 nesting pairs of birds across at least 20 species, many who build their nests just feet away from the boardwalk:
And they fly back and forth with their nesting materials so close that they occasionally hit people in the head with their wingtips or dangling branches:
The birds even take breaks from the nests to rest on the boardwalk rails, and don't pay any mind to the people walking by within a few feet:
Sometimes, even a very still person can be a great resting spot:
Not just birds either - here, an otter popped out of the water right between two people walking towards it - rolled around, played, then jumped back in the water to watch us pass:
Your walk on the boardwalk can be interrupted by wildlife crossing:
I know it's a limited crowd, not everyone's into birds and wildlife, but I think a nominal charge of $10-20 to access a place like this while at Disney would get plenty of takers, enough to cover the cost of maintenance - and the little restaurant near the dock could charge typical Disney prices enough to pay for staff. I know I would pay to visit this place pretty much every time I was at Disney.