MacOS – Scale screen on custom resolution

PS This is not a question about the basic functionality of scaling or changing the resolution of the screen.

The screen:

  • Specs: 23″ 4K 60Hz
  • Ports: HDMI (supports up to 4K on 30Hz, 2K/FHD on 60Hz), DisplayPort (up to 4K 60Hz)

Original problem:

For some reason, I want to connect the display through an HDMI cable, not DisplayPort, and since the MacOS by default sets the resolution to 4K (max allowed res) and scales it to “look like” 1080, the refresh rate is locked at 30Hz (which is quite horrible)

So from the settings, I can set a custom resolution to 2k (the one with “low-resolution” label, since the other 2k option only changes the DPI), which then allows the screen to run at 60Hz, but since the screen is only 23″, 2K makes everything too small

Or I can set it to 1080 (the one with “low-resolution” also) and everything should be fine (both refresh rate and UI size), but the screen looks really bad and washed out, apparently my monitor doesn’t support this resolution very well.

So this takes us to my question:

Can I set a custom resolution, AND make it scale to look like another resolution?
For example, change the real resolution to 2k, and change the DPI (scaling) to “look like” 1080?