I agree that you won't achieve satisfactory output given those constraints. Best bet might be a sub that's thin enough to hide behind the couch or to use as a riser, like a Danley THSpud; or to use subs as end tables, hidden in plain sight -- maybe a pair of rosewood Hsu VTF-3. Either way, your budget will be blown. You could also build subs yourself that look like furniture, maybe a pair of twelves disguised as end tables, or a 15 made to look like an entertainment center? Or maybe you could try running a pair of Dayton 1000L low profile subs nearfield between the wall and the couch. Nearfield subs take a lot of time, patience, and effort to blend with each other and with your mains, but it can be done. Plan to add a miniDSP and UMIK-1 to your shopping list if you choose this path.