You don't really need to refer to the stage. Stop doing things stupidly and you won't have problems.
The document class status doesn't mean it should be the main class. In fact it's normally tiny.
In a finished (properly built) app, it'd just add the preloader, then switch to intro animations, then switch to the menu class. The menu class has some buttons, sets some settings (in another class), then triggers the initialization of a game which takes the settings and builds the game facilities, then triggers a class that handles the game loop.
The point is, don't do everything in the main facade singleton document class of doom.