Doors and walls are the only map elements that must be part of two rooms (or a room and a corridor) at the same time. Hence, walls and doors are the only elements that must be subject to multiple, incongruous rules of perspective. Forcing the walls to be part of multiple, separate perspectives creates some visual confusion. But, because they're everywhere and obviously the only division between rooms, the walls remain recognizable as walls. They're a little disturbing with their double sides, but they're clearly walls.
When I drew the doors in double perspective, they stopped resembling doors at all. They looked like strangely distorted red treasure chests. I tried adding handles and door knobs. I tried all kinds of things. Nothing worked, as the examples attached demonstrate. The problem grew worse where a door fell between two rooms whose vanishing points fell in completely different directions, twisting each side of a door in wholly different directions and creating absurd looking shapes. I don't have an example of this saved. The door on the left in the third image below comes closest, but that's not an extreme instance. Imagine a door with one side reaching up to the right and the other side reaching down to the left. Ugh!
So I decided to remove them from the whole perspective issue and just make them red rectangles. The result is less than perfect. But it was that or abandon the larger project. Anyone have a better idea?