Clone monitor with different aspect ratio using black bars

My situation is very similar to this question except I'm looking for the solution with black bars.

I have a laptop with a 4K internal monitor (resolution 3840x2160) connected to the xorg output eDP-1-1. I often connect a videoprojector on HDMI-0 with a resolution 1280x800. Meaning they have a different aspect ratio.

I know of the options --scale-from and --scale, but unfortunately, they either stretch the image or enlarge the frame buffer (the size of the screen in Xorg jargon) and make one of the monitor clip the image. The --panning option is also unsatisfactory as both monitors don't display the exact same thing at the same time. I would want my students to see the same thing I see.

I'm currently using --scale-from and stretch the image as both aspect ratios are close enough for the stretching to not be noticeable on regular text. But ideally I would like to have black bars on either of the monitors so that they both display the exact same thing without distorting the proportions.