Here's what I did in the end: I decreased the resolution of the laptop screen to 1920x1280 by keeping the aspect ratio of the original screen (3:2).
I added this to ~/.xprofile
:
#!/bin/sh
xrandr --newmode "1920x1280_60.00" 206.25 1920 2056 2256 2592 1280 1283 1293 1327 -hsync +vsync
xrandr --addmode eDP-1-1 "1920x1280_60.00"
This config behaves well when the external FullHD monitor is plugged or unplugged. However this doesn't apply to the login screen which looks awkward nor to other users if there are any.
The new modeline was generated with cvt 1920 1280 60
.