This shouldn't be an issue even today (aside from being horribly expensive.)
Take inspiration from Minecraft, and use a grid structure of "blocks". I'd use 3 "floors", and just fake the floor traversal. Because you're not getting to kill me (the villain) just because you managed to traversedtraverse 6 floors...
Bottom floor is essentially just hydraulics and cable management to lift the various blocks up/down to create the room and passages. It can even include pitfalls by going further down than the rest of the floors. The randomness is just an algorithm, they do that already in the various rogue-like games.
Middle floor is the maze itself where the people get lost. The floor traversal could be a winding stair that just slowly move up/down as the people traverse it, giving the impression of changing floors while the rest of the maze re-arranges itself.
Top floor is all your traps, monsters and goodies being shuffled around by warehouse robots, then dropped down in the respective rooms by a hatch in the ceiling. Simple enough. Upon re-arranging the maze, the stuff is pushed back up again by the rising floors.