The program 'nvidia-settings' received an X Window System error.xrandr to the rescue! Turns out it's not just for screen rotation and reflection; it can also do resolution and refresh rate:
This probably reflects a bug in the program.
The error was 'BadValue (integer parameter out of range for operation)'.
$ xrandr --output HDMI-0 --mode 1920x1080 --rate 24.0
(Try running it without arguments to see what resolutions and refresh rates are possible)