Been thinking about this, had an idea. They probably wouldn't do this because it's a little too high-concept, but I'd love to see it.
Basically, the idea is that the Disneyland or Magic Kingdom that we know is just one corner of the "real" Disneyland that intersects with our world. The current logo that appears before Disney movies, where the castle is surrounded by miles of forest and there's a pirate ship on the river and steam train off in the distance? That's the real Disneyland.
So our hero or heroes would take a wrong turn somewhere in Adventureland and slip into that world. Here, the Jungle Cruise animals are real, the skippers aren't acting, and the jungle stretches for miles. Off in the distance they can see Cinderella Castle. Frontierland would be much the same way, a sprawling desert filled with cowboys and bandits and runaway mine trains. Tomorrowland would be a real city of the future populated by robots and aliens (that incorporates EPCOT Center of course!), Fantasyland would be an actual medieval town with surrounding enchanted forest. At certain locations, the walls of reality are a bit thinner and this Disneyland connects with ours, allowing the characters to travel between the worlds.
I think it would lend a bit more grandeur to the idea of The Villains taking over. They're not trying to control a theme park, they're trying to capture an entire world.