Okay, I'm actually here in Escondido now, so let me fill in some of the details I was missing.
Looking again at the room, I think this wall will be the best location. It's about 105" x 96" of pure wall space. If you put the bottom picture from post 5 on the left, and the top picture from post 5 on the right, you'll see the wall below.
There's one window to the right, and two further along the wall (you can see the first of the two in the corner there) but I ought to be able to hang a sheet of TWH that covers almost the whole area across, and should leave a good bit of room top and bottom (the wall is just about 8'' high, so I should have 2' top and bottom.)
I couldn't fit a whole TWH in the other portion of the room, and I'd rather move the location than sacrifice more screen space.
I'm going to paint the wall that the screen is on a dark blue, and maybe line the screen to try to absorb some ambient light. I'll also have blackout curtains over those windows. The rest of the walls will be a medium grey, which should also help with ambient light.
I should have something like 10.25' - 10.5' of throw distance from the back wall. Ideally it'll shoot over the couch and hit the board just about center, and I can adjust a bit with the zoom and the vertical adjuster as needed.
Does that seem like a reasonable plan? What's a good way to affix the TWH to the wall without damaging the wall too much (it's a rental)?