Or maybe a little bit of both? While the lightmap baking will produce high quality shadows, the rooms will most likely loose most of their customizations. But, as thinking in terms of level streaming, only the content required for the current room the player resides have to be rendered, and the rest can be queued to be executed later as the player progress forward in the maze. You can also remove some rooms from the scene the player left behind, so you will end up only with a few rooms in the scene to be exists, and that will most likely be a nice optimization since you can cut down the physics and actor processing costs significantly.
Btw i have checked the game, looks very cool! There also is a nice graphics settings ui that helps to cut down the costs, althought with HIGH settings on everything, on my gtx 1070 i got ~70% GPU usage with 60fps (vsync), so this is running smoothly here already.