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.