> So it sounds like I might need to render the floor as one sheet and walls as another?
Damn, yeah; this is the misunderstanding. This was my intention: walls and floors on separate layers.
Compare: "When you want to draw the floor" and "When you want to draw the walls" in https://github.com/godotengine/godot-docs/issues/3316#issuecomment-614923124 and you'll see how only one of them resables our walls.