campaign development – How to design a maze without it being a time sink maze and unfun?

I was planning a 1e The One Ring game where the party gets trapped in the mines of Moria and have to get out. I had asked a question about the roles here. After discussing it with others, my idea of wandering an actual maze with multiple levels and various puzzles has been pointed out that its likely to be dull and boring for the players.

I am at a loss of how to run a maze, without it being an actual maze.

It was suggested I could use a position scale which would determine how the party was doing within the maze. Various challenges and checks would adjust the score as needed. It holds some merit, but one of my big surprises is the 3rd (and secret to the PC’s) exit which is the endless stairs is going to be really hard to work in if I did it in such a way. Plus, how would the PC’s really guide their route to one of the potential exits if their not actually wandering a maze that was designed? Granted, not having to create a 40 mile by 10 mile by 4 mile maze sounds rather nice at this point.