It’s just physically impossible to get equivalent OLED HDR on a projector. Just the way the technology and physics work. Even movie theaters claiming to display it are not really doing so. The inverse square law prevents that and light bounces off the screen so pixels are never truly black.
It’s why when I have seen tech trade shows or gone to ones myself they are always demoing giant LED screen tech. Sony had one at NAB (National Association of Broadcasters) a couple years back of their Crystal screen. Was 4K HDR on like a giant cinema sized screen. That was mesmerizing.
Same NAB I Listened to a talk by a some big cinematographer there about how theaters would need to rethink movies and do away with projectors for HDR and use a system like Sony’s Crystal tech.
Only downside right now is cost. Right now it is just more cost effective to do 4K projectors. (Which BTW some theaters are still only 2K.)
What I will say it sounds like your setup is still probably leaps and bounds better than what you would get going to most cinemas.
The TL;DR I am jealous.