Your projector will have maybe 150-200 nits if it is an expensive projector. It it isn't expensive, it will have even fewer nits. UHD Movie content is mastered with monitors having 1000 or 4000 nits. A great 85-inch flat screen TV costs maybe $3000 and will produce as much as 3000 nits (Vizio). The additional brightness does not appear on-screen as 100% white. Instead, the additional brightness is used to create colors that cannot be reproduced with less light (like a projector--projectors simply cannot reprodce most of the expanded color space available with UHD/HDR content). This effect is NOT subtle, it is VERY obvious. A bright projector has a markedly smaller color space than a bright flat panel TV. The projector has an optical system that degrades the image, flat panel TVs do not, you see each pixel with PERFECT precision. This makes projection look pretty terrible on UHD sources compared to good flat-screen TVs. As long as you understand that... A 10-foot wide screen in a 10-foot wide room leaves no room for the frame of the projection screen. Be careful with measurement requirements. Be sure you understand the difference between image area and the full dimensions of the screen with the frame included. A room that narrow has serious challenges. Side surround speakers and any other speaker closer than about 6 feet from the/a listener should be dipole speakers so no sound is radiated straight forward from the speaker. That keeps the "close" speakers from being able to overwhelm a close listener. No matter what anybody else says, in your room, the only correct loudspeaker for your side surrounds is dipole speakers.
Dolby's immersive system (Atmos) is the worst of your 3 audio options. DTS:X speaker location recommendations are 50% better than Dolby recommendations. But the absolute best locations for the immersive speakers follow the Auro-3D recommendations where the side surround height speakers are at the ceiling/wall corner, directly above the side-surround speakers. The front height channels should be located directly above the main front left and right speakers, hanging from the ceiling. NEVER use ceiling-mount speakers that aim directly down. Use box speakers (without a port on the back since you might block the port with close-to-wall placement) ALWAYS if it is possible. If you don't want to install speakers permanently on wall brackets, you can hold the speakers to the wall bracket with generic bungee cord (without hooks, tie knots). If your surround processor or AVR does not support Auro-3D, I would dump it immediately and get a new one that DOES support Auro-3D because using Auro-3D on an Atmos or DTS:X soundtrack SOUNDS MUCH BETTER than using Atmos or DTS:X decoding respectively. In fact, without Auro-3D decoding, I wouldn't even BOTHER with immersive sound. Atmos is PATHETIC for sound quality and DTS:X is only a LITTLE better. Auro-3D is WILDLY better sounding even when the soundtrack has no Auro-3D soundtrack. If I did not have Auro-3D decoding in my system, I would feel like having height speakers was a waste of time and money.
Example: In Star Trek: Beyond, there is an attack on the Enterprise with hundreds of 1-man alien ships landing on the Enterprise hull, drilling through the hull to allow the 1 passenger to enter Enterprise fighting. There's weapons fire from every direction, shouting, banging sounds, drilling sounds, all the mayhem you might expect on a starship being over-run, one enemy at a time. But with the standard US soundtrack (I forget whether it is Atmos or DTS:X), the ONLY thing you hear during the ENTIRE battle sequence is the computer saying "Red Alert"... aside from that, the height channels are SILENT during the battle. When you switch to Auro-3D processing, there are ambient sounds in the height channels for 100% of the battle sequence, including the computer announcing "Red Alert" but now adding reflections of the yelling, drilling, weapons fire, etc. In short, Auro-3D decoding sounds better than Atmos or DTS:X decoding, even if Auro-3D is not encoded on the disc. Auro-3D decoding makes EVERTHING sound better. It fact, it is so good, I won't listen to music in stereo any longer. Everything gets played with Auro-3D processing. This is the first time I've ever been able to say that. Dolby Surround (Atmos' decoder for non-Atmos sources) sound ****** in comparison (grey, dull, anti-musical, dry, opaque, lacking dynamics, boring). While Auro-3D processing of stereo music sounds live, vital, musical/tuneful, bright, open, spacious, and smile-inducing. If you don't have Auro-3D decoding/processing in your processor/AVR, I would suggest not even bothering with the height channels, you'll just be disappointed.