ZDoom

Lacking other evidence, it must have been a driver issue. Updating from last month's AMD drivers seems to have fixed the issue, no refresh resetting going on from attempts to fullscreen or launch in fullscreen. Only GZDoom triggered this issue, though.

That's because GZDoom doesn't change the monitor resolution or refresh rate at all. Fullscreen is simply just a borderless window covering the entire screen. Windows itself detects such a window and makes some changes, mainly turning off DWM, but that's all behind the scenes and nothing GZDoom itself is doing.

Try upgrade your display driver. It really sounds like it has some very nasty bug. If that doesn't fix it, report the problem to them as this is either a driver or OS issue.

Not sure whether this is because of cruft, a missing/unimplemented feature, or something I'm missing, and the lattermost seems really likely when I can't find anyone else on the board wondering why GZDoom changes the refresh rate of their spiffy 144hz monitor back to 59hz whenever fullscreen is enabled. I can't seem to find any cvars or options that keep GZDoom from doing this, either.