If the distance from wall to screen is 12.9' (154.8"), with an HT3550 or similar (depth 10.3" + 4" for cables = 14.3"), the available distance would be 140.5".
An 120" screen (16:9) has a width of 104.6". This would result in a 1.34x throw ratio. With an 110" it's 1.46x, and with 100" its 1.61x.
Wouldn't the XY BC 0.8 hotspot on the first two sizes at least?
How about using curtains for the windows, lights that don't hit the screen directly, lights that are only present (during viewing time) in the seating area and not the screen area?
A light grey or even white screen could be used.
A light grey screen would benefit from a brighter projector.
Percentage wise, how much will the setup be used for sports than other types of content?
Depending on how much ambient light remains in the room, even a HT3550 could be used here. Other DLP's with RGBRGB color wheels would be Optoma UHD50/51/51A/etc, Viewsonic PX7274K.
For brighter DLP's the Benq TK850, Optoma UHD51ALV/52ALV, ZH403, Viewsonic PX7474K, LS700-4k.
Some people are ok with 3LCD for sports as well. Depending on the percentage of total time dedicated to sports, a 3LCD could be an option. Epson HC3800 paired with a grey, not necessarily light grey screen could work.
The Benq's would be most accurate out of the box, with the Epson HC3800 probably last.
The HT3550, TK850 and HC3800 have active irises that improve black level.