Axiom Home Page Forums General Discussion Advice from Axiom Owners Hanging QS8's without a stud?

What I'd do in your case is attach a piece of wood (1" thick, edges rounded off with a router, and painted to match the ceiling) across two studs/joists in your ceiling so that it intersects your desired mounting location. Do this for each mounting location and then attach the brackets to the wood.

EDIT: After seeing your pictures, it seems you wouldn't even have to route the edges. Just cut the wood to fit between the rear wall and the existing beam. Depending on where the joists are, the wood may need to be rather wide.