Popping in to give an update before calling it a night!
First of all, thank you for all the help! I've been reading through all the comments here and trying a few things out. The first thing I tried was switching the default desktop environment from the default Gnome to KDE. I much prefer KDE to Gnome since I have experience with it on the Steam Deck, so this is the solution that I had the most hope for. Sadly though, things are much worse in KDE. Unlike in Gnome, KDE has the terrible screen tearing that was mentioned in X11, but is still similarly unable to support running the monitors at different refresh rates. Since a lot of the comments here mentioned Wayland though, that was my real end goal in getting KDE installed. Unfortunately, witching over to KDE Wayland, things became significantly more unusable and it was about the same experience I had while trying to install Nobara. Both displays were totally unresponsive for seconds at a time and I was only able to interact with things during brief moments when they would stutter along instead. This was pretty painful to log back out of and was an overall mess like a couple of you had mentioned it might be.
I went back to Gnome after this. Since KDE didn't seem to be they way forward, I figured I might as well try enabling Wayland on Pop_OS's built in solution. Wayland support was hidden by default on NVIDIA as mentioned, but one quick config edit later and the option appeared. Things seem to be going much better now! I'm running Gnome Wayland right now and while things aren't flawless yet they're significantly better than before. Both monitors are working at their full refresh rates now without any screen tearing or flickering. As for gaming, so far I only have Helldivers 2 installed running through Proton, and performance is about 8% worse than in Windows on the same graphics settings while on the ship. I am also getting an odd visual bug where the in-game menu looks like it opens and closes very quickly every once in a while. It's not actually open or intractable though, it's more like the game randomly displays a single frame from when I did have the menu open to change the graphics settings. Tomorrow I'll try enabling Proton experimental and see if that fixes anything, and also try installing some more games.
I'll come back again to give an update on how things are going then! I'm still lacking HDR and there are other bugs that look like they need to be ironed out, but I'm much more optimistic about this than I was before. I think I'll keep dual-booting for now, at least while I'm still trying to get everything working properly, and hopefully that next version of Pop_OS brings HDR support. For now, it's at least nice to know that different monitor refresh rates are working.