Your seating area is 12x12, but your listening area is determined by the walls. There's no way to remove the acoustic effect of the large opening behind the seats without adding a wall, so take advantage of it, and the doorway to the right. These spaces will suck out bass, but they'll also smooth bass modes as a result. Stick construction has advantages in this regard as well. Good sound doesn't require a dedicated space, just a little care in setting up the space.
Since you have location options, I'll point you to Welti's analysis that identifies 3 optimal choices
- 4 corners
- 4 midwalls
- 2 mid side wall
My room has the screen on the long wall, with a doorway and a fireplace on the side walls, so my subs are front and back, offset toward the fireplace but not in the corners. Measurements show very benign low frequency modes, but with the telltale of a secondary resonance - the leakage through the doorway - at a frequency too low to fit in the room. Bass response is very flat below 40Hz, with rapid temporal decay and mild room modes. Above 40Hz is lumpy, and above 100Hz fairly chaotic, but that's not subwoofer territory.