Toby,
Sorry but that winner idea will unlikely work. First, you have to place the mirror well into the middle of the room. Second, depending on the geometry of the projector/mirror/screen, the mirror size can be fairly large. Third, even though the mirror is on the direct light path, you will still be bothered by the scatter light coming from the projector that is facing right at you.
I still think the shelf mounting the projector right behind and above the main viewing position would be the best solution for you (unless you are serious about using the back room).
