I just discovered a couple potential (temporary) fixes.
The first: switch to a lower, 4:3 resolution. Then, change the scaling setting to "Use fixed aspect ratio scaling". Next, switch back to your normal resolution. Haven't tried that yet myself, but it supposedly will keep it there (for some people).
Another trick that people have found is to turn off your monitor, restart your computer, and then give it enough time to get to the login screen (or until you hear the Windows chime, if you don't have it set up to go to the login screen when turned on) before turning your monitor back on, and then apply settings accordingly. For some people, removing the monitor from the Device Manager first, before restarting, seems to work.
EDIT: For now, the first fix seems to be working for me.
EDIT #2: The scaling didn't work with a 640x480 game that I tried, but it did work when I put Fate/stay night (which is
00x600) in fullscreen. Since
00x600 is on the list of supported resolutions for my monitor, while 640x480 is not, it may be that scaling will not work for nonsupported resolutions. (A note: I'll probably still play F/sn in windowed mode, because text, etc. looks sharper to me than in fullscreen.)
EDIT #3: ...I did not know that Half-Life (the original) could be played in widescreen resolutions. *shrugs* You learn something new every day....