I still haven't received any BSODs (this is the longest I've gone since they began). So I believe we may have resolved the issue!
Thanks also for confirming that I could still use GeForce Experience to update my graphics drivers. I've since done that as well, with no issues. I think seeing "Nvidia" on each made me hesitate.
I'll leave this thread open a few more days, and if no BSODs occur, I'll mark this resolved. Thanks again to both axe0 and valihrach for all the help!