Update: driver just crashed, again, on 1680x1050, confirming it is not a resolution issue.
A new revelation: games are not crashing due to resolution problems on my end, but due to running in full screen mode as opposed to windowed mode. For whatever reason, if I run a game at 1920x1080@144hz fullscreen, I crash. But I run at the same resolution and refresh rate in windowed mode, I do not.
My only conclusion is that there is a clear problem with AMD's display drivers.