I tried Duke's suggestion this morning . . .
I have a spare bedroom with about those dimensions (actually 12x13x8) that I had set up a spare system in, just as an afterthought when my son moved out. Components are all spares not even close to your budget - I'm using a TAD60 amp, Von Schweikert VR3 speakers and a Marantz cd changer. I had it set up square originally and found it ok, but unremarkable. Moving the speakers out into the room didn't materially improve performance.
After rearranging per Duke's advice there's a huge improvement in imaging and bass performance. Thanks Duke! I have the speakers set up at about a 20% angle and they're pretty well hugging the walls right now, though I will be playing some with placement in the next day or 2.
The results now are good enough to entice me to put my spare turntable back up there and do some more tweaks - particularly on furnishing. I may even invest on some equipment upgrades.
Thanks for the thread, and thanks again Duke!