Apple - Is it possible to force the MacBook Pro HDMI output to specific resolution/refresh rate?

The answer is: Yes, this is possible.

I found a piece of trialware called SetResX that lets you set arbitrary real resolutions on the HDMI output, and it works!

I also found a video tutorial here that explains how to do that yourself with a substantial bit of effort, and without the nice UI, but I haven't tried that method.

Additional answer, to combine with @ruief's answer to use SwitchResX (which I agree works really well, having found it from @ruief's answer and tried it!):

• Be sure to use a Mini DisplayPort (i.e. thunderbolt) to DisplayPort connector, not an HDMI to HDMI connector - you will likely find a lot more available resolutions; namely, everything that the monitor and MacBook can support which is higher resolution than 1920 x 1080 (aka 1080p)

I am not sure if the above is different between MacBooks? It made a huge difference on my MacBook Pro Retina 13-inch Late 2012; adding genuine resolutions (i.e. as reported by the monitor's OSD, not just scaled displays in other resolutions) up to 2560 x 1600 60Hz - which just weren't there with the HDMI cable.

You might also want to check out this article by Stephen Foskett, which recommends enabling MST-mode on the monitor itself to access even higher resolutions on older MacBooks. However, in my own case I can report that I did not have to enable MST, and that I did eventually get a perfectly usable 4k (3840 x 2160) 27Hz (!) mode (genuinely, as reported by the OSD of the monitor itself) working on my Late 2012 Intel HD Graphics 4000 MacBoo Pro with an ASUS VP28U 4k monitor!!! Definitely no way that could have been achieved without SwitchResX!

Finally, it's also worth noting that another tool, simpler to use than SwitchResX and without the ability to define new modes, but still with the ability to show the 'hidden' resolutions, is RDM which can be installed via a download link from the GitHub page, or via Brew (brew install avibrazil-rdm).