It took me forever to figure this one out (about 2 months total), but thanks to the Windows Performance Analyzer I was finally able to find the culprit. Symptoms
The game will play fine for about 20 minutes, but the longer you play, the more frame drops you'll experience. Eventually, you'll start getting audio glitches. Certain sound effects will start to lag behind during big fights (and then all rush in at the same time if you pause the game), or you'll hear some sort of static crackle coming from the any audio source (be that from the game or from another background process like your music player). Then, if you quit the game (either a normal exit, using the "fast exit" option in NVSR, or even force quitting the game), your CPU will start to do something in the background (in my case, it would sit at around 30%). Task Manager would not find a single process using that much CPU power, but if you use another software called Process Explorer, you can see that FalloutNV.exe has not actually closed completely (even though Task Manager doesn't show it anymore).
During this time, any other application you try to use will be slowed down. If I try to open Chrome, the computer would slow down to a crawl as it struggles to open that application for about 5 seconds. Then it opens it, and it'll be sort of ok, but still sluggish. Any other big application that I open will trigger the same response. If you have audio going you should hear the static crackle sounds I mentioned earlier whenever the CPU is used more heavily. Also Mod Organizer 2 and Steam will both report that FalloutNV.exe is still running.
After about 10 or 15 minutes, FalloutNV.exe will finally close and your PC will go back to normal (the longer you played the game, the longer you have to wait for your PC to recover, but I definitely never had to wait longer than 20 minutes for the PC to recover).
I recorded a little video of the symptoms happening: https://youtu.be/C_xPG_n0huQ How I found the culprit and solved the issue
I played for about 20 minutes to trigger the issue, then I alt-tabbed out of the game and turned on Windows Performance Recorder. Then I went back to the game for a few seconds and quit (triggering the annoying high CPU issue with audio glitches). I recorded for about 3 minutes and then stopped. I put that recording into Windows Performance Analyzer and this is what I got: https://i.imgur.com/QlMQKLl.png
The bottom graph is the GPU usage, and as you can see, at around 13 seconds, FalloutNV.exe stopped using the GPU entirely. That's the moment I closed down the game. I highlighted that time in green.
The first graph is CPU usage, and as you can see, as soon as FalloutNV.exe closes (when the green highlight ends), the CPU all of a sudden goes up a little and stays at about 12% constantly for the remainder of the recording (WPA doesn't show me much info past a couple of minutes anyway, the graph ends at about 196 seconds). Then, I opened up the FalloutNV.exe to see what processes were running on it and preventing it from shutting down and lo and behold we have "PSINAflt.sys" running from the second I exit FalloutNV.exe and stays on the whole time (it's highlighted in blue, and that blue stretches all the way to the end of the recording). A quick google search tells me it's some process from Panda Antivirus. I go and uninstall it and that's it. The game is fixed. I went ahead and ran the game for about 4 hours (playing a bit, alt-tabbing out, coming back later to play some more) and those issues disappeared completely.