It started as a mix of role-playing and game mechanics, but has now switched to game mechanics completely. So someone needs to move it to the wishlist.
The exact number of gates(/doors/portals/holes/mouths/mirrors) you would need to randomly enter to hit this limit would need to be tested and tweaked heavily, but it should be a multiple of the number of rooms you would need to pass through if you choose your path wisely (perfectly). Probably 8x-10x or so. When you hit the limit on the number of rooms, the next portal will take you to the room that lets you out, and you should get a message like "Your (eternal|steady|meandering) perseverance, symbolic of life, has taken you to your goal of life." What your perseverance is called would be based on the rate at which you went through doors, and whether or not you logged off for a day doing it.
For each room, there should probably be 3-7 entrances and exits, and each one of them corresponds to a kind of path. At the beginning, the guardian will tell you a riddle like "Take the path inverted to the great tree." "Hold to the side of light, on your journey." "Lightning arc and lightning spark; be bright and then be dark." "Fire guides you from here to the lake, and then you must be the fire." "Find the flower, take the cup, drink deep and go up." "Take the knife in the dark as long as the dark keeps you." Each of these is a rule that tells you which path in any given room you must take. They are meant to also give you an idea of how long your trip to Dakkru's realm will take, as some riddles are shorter than others. Completing the last example, it means that every time you come from a dark entrance, find the exit that either uses a knife, or represents it. Once you come from a bright entrance, take any exit but the knife.
The exits can be anything from a carved archway, to a fireplace, to a green bottle labeled "drink me". There could be in-dungeon item requirements, like taking the flower, actually picking up a knife, finding a torch. Those last two would probably be more like shortcut items, as you can use them to make a right exit. (The cup refers to a book, with a cup embroidered on the cover.)
I really do love this idea.
