How do I hang a shelf without drilling holes?
A "C" (or perhaps "[" is better) shaped shelf could sit under and behind the couch, keeping it no more than an inch or two (even less if it was metal plate for the section behind the top edge of the couch) off the wall, and holding the projector above the couch without needing any attachment into the walls.

Not exactly what I'm thinking of (not having much luck thinking of the right search terms to find what I am thinking of), but the general idea - legs that can slip under the couch, standards, a shelf.