There is no way to ever completely solve your problem. Acoustical physics have certain rules that are constant. Still one question I have is what kind of speakers do you have or plan on using ? Your speaker type (not "brand" but the way the speaker works) may go a long way in overcoming some of your difficulties.
Do you plan on using Bipole, Dipole, or direct radiating speakers ?
You say it's approximately 10 x 12 which is equal to 120 square feet but what is the true square footage of the room ? How tall is the ceiling and is it flat ?
How far is the front speakers from the seating ?
Can you/will you hang speakers from the ceiling ? Is the room acoustically active (lots of echoes) or acoustically dead ?
Do you have 4 friends who are willing to hold satellite speakers and move them around at your command as you experiment with best placement ?
Have you considered brining in a professional ?
I have to say that with viewers sitting at different angles it sounds like you will have problems just getting an front sound stage.
Try posting a reference picture on yahoo photo album and give us the URL. Can't promise anything but this might help us help you.
First off, I know everyone has differing opinions on the effectiveness of 7.1 (over 5/6.1). However, the shape of my room vs. the seating arrangement gives me a challenge in ANY case, so I've opted to give 7.1 a whirl. I think more speakers might be better in this case.
I have a diamond-shaped room (small room, equivalent to about 10x12), with the tv at the top, and the listeners seated on a sectional couch at the bottom point of the diamond. The long end of the couch is on the right wall, and the shorter end on the left wall. (If you draw a "check mark", that's basically the shape of the seating position.. two people would sit along the left side, and 3 people on the right). The TV wall is angled more toward the people on the right (long side).
Technically, there is no 'back wall'. I HAVE pulled the couch out a little bit from the wall. The right side is long enough where I can wallmount the RIGHT surround speaker and fire it directly down the line and slightly behind the listeners. My problem is the LEFT surround. To accomodate all the listeners, one rear (back) surround will be high up on the right wall, and the next rear surround makes it's way to the bottom corner, making sure to get one back surround on each side of the center/sweetspot. The listers on the left are slightly facing a different direction (and, so are there ears). Should the LEFT side surround speaker be behind them on the left wall, facing the other side surround? (in which case, it would be in FRONT of the listeners on the right wall). Should it be aimed toward the back corner, where the other back surround was placed? (so that it's firing in their left ears?). BUT, that may take away from the listeners on the RIGHT wall. Or, should I aim ALL speakers out, on all walls? Or, perhaps just that one speaker I will need to experiment with (just that left surround.. facing forward, backward, out, etc?). I know, the goal is "enveloping sound", so symetry is probably more important in this case, rather than worrying about whether or not the left surround speaker is in front of, or behind, the majority of listeners.
This is nearly impossible to explain without a picture. And, yes, I will be getting a receiver with an auto-setup and EQ. Just wondering if anyone has had a similar dillema, and how things worked out for them.