I think this would be possible. I have a room that's 25 by 14 and I have a 96 inch screen. While this seems to have nothing in common with your situation, it actually does. My Panasonic 900 projector, mounted on the ceiling, is about 8.5 or 9 feet from the screen, and the screen is around 85 - 90 inches diagonal (16 x 9). All the theater stuff is mounted in the front half of my room, and the rear half will be a games area (several dollars from now).
More importantly, we sit right under the projector, or maybe back a tad. The whole thing works, at least for the picture. Having a smaller screen also wouldn't kill you - you'll still get the experience.
I think the acoustics will be the challenge. The mains and center are no problem, a small sub woofer should suffice, but it's the rear effect speakers that is the uncertainty from my perspective. There is no "rear" in your room. My rear speakers are about 5 feet behind our ears on the ceiling, about 10 feet apart in total.
I would simply mount your effect speakers in the rear corners of the back wall, angled towards your head, and live with it. It might be better than you predict, once they're balanced as well as possible.
Anyway, not much choice as I see it. I hope you get a few more answers, because I'm no ace on this, and I'm learning too. I don't know much about bi-directional effect speakers, for example. Might they serve well here? I'll leave that for the next who replies.
Go for it and enjoy. Cheers, Tom.