Assuming one could get the floating/artificial island set up in the first place, sport-tourism could be one way to bring in hard cash.
Bloodsports: cage matches, martial arts competitions, dueling.
Hunting: you could recreate “Monster Island” from the old Japanese monster movie. By importing breeding pairs of large predators normally off-limits to hunters, and managing them much as farmers and ranchers manage stock. As it was pointed out on some website I was on recently: dogs and cats, cows and chickens are in no danger of extinction, why are tigers? Because people don’t have any financial incentive to breed and maintain them. They’re sacred to the environmentalist religion, it’s considered unethical to harvest them, even if it would lead to their preservation. It’s the same reason they burn ivory from poachers in Africa, and it makes no. bloody. sense. at all. It just drives up the price to the point where popaching becomes a worthwhile risk.
You could solve the problem of at least a few populations by maintaing a breeding pool and exchanging them: komodo dragons, tigers, what-have-you. Create a whole menagerie of unusual beasties: salt water crocodiles, Galapagos tortoises and sea-going iguanas, sea turtles, primates. Encourage pinnipeds and use them as part of your ecosystem for feeding the large predators. Practively manage all of these creatures as resources, helping them where needed, pruning when necessary.
You could even take in all those stray dogs and cats PETA euthanizes every year, and let them either survive or feed the predators- strongest survibve.