I left a comment before about when you complete all the puzzles it will open up more puzzles. Now, with that said...
I started thinking about it, and maybe it sounds silly but I mean, how big can this island be? I'm not even sure if the 3rd takes place on the same island? I'm assuming it does. So why not after all the initial puzzles are completed the villagers find a way to go to another part of the island with more puzzles, like have 3 or 4 little additional parts to the island, and then once those are complete there are puzzles that require access to all parts of the island? That would keep me busy for a while \:\)