To determine size, I'm just going to hang a sheet or something and twiddle with different sizes until I find one that seems appropriate for that distance.

Also, I remeasured the room, and the measuring tape grew a little in length because I get 11 x 12 instead of 13 x 14. (I was looking at the inches side which popped out at me and somehow the 1st 2 characters of that got interpreted as feet.) So the throw is now going to be about 10 feet instead of 12, which makes maximum possible screen size as 106 inch diag. instead of 115.