In my theater, I have ambient light and need to change it back from a theater environment to a den environment from time to time. I have a motorized screen that extends out from a boxed enclosure in front of a bay window. It retracts when I want my den back.
The screen is a 120 inch diagonal 16:9 screen. My projector, a Sony, is mounted a little over twelve feet from the screen. In my case it's actually mounted in the garage behind me, and projecting through plexiglass with a little rectangular cutout so the image only travels through air from the projector to the screen.
Measuring from the bottom of my screen enclosure to the floor, it's seven feet. In fact, I have it so it stops at about 16 inches off the floor. Still can get well over 100 inches diagonal on a 16:9 image. The available vertical for my screen is 4.8 feet and the available horizontal is 8.5 feet. That gives me a diagonal picture, if my math is right, of over 115 inches.
You have eight feet to play with for your screen height. You also have a black room. Were I in your shoes, I would think seriously about a 150 inch diagonal screen.
You can get a 120 diagonal in there pretty easy, assuming your projector placement accomodates it.