I did a very brief test due to lack of time, but disabling everything except City of Heroes seems to have fixed it. I'll report back when I have more time to test things. The only things open in the background, which I exited out of, were Steam, GeForce Experience, Discord, and Zoom.
Now, Steam, Discord, and Zoom don't utilize the GPU at all, so if I had to guess what was messing things up, I'd say it's GeForce Experience.
(Edit: the problem continues. See below)
Like I said, I'll play around with it and report back when I have the culprit identified, if for no other reason than for posterity.