I tested two EDID emulators and both of those worked: ATEN VC080 and ATEN VC081A. With both I first connected to a display that supported my target resolution 1920x1200 and worked properly with iPad. The EDID emulator then learned the EDID profile from that monitor. Then connecting to the monitor that used to have issues iPad selected the correct resolution because the EDID profile was now coming from the emulator instead of the monitor itself.
Please note that different USB-C adapters seem to behave in a different way. With the Apple USB-C Digital AV adapter the EDID emulator did not help, and iPad still chose to use the wrong resolution 1280x1024. Another brand (Linq 6 in 1 USB-C multiport hub) worked fine.
At least for my use case the EDID emulator does the trick, and I'm able to connect to the monitor that I want and get the proper resolution.
ATEN VC080 is more versatile and stores up to three profiles and allows even manually editing the profiles to add or remove resolutions. Editing requires connecting with a RS-232 interface to the emulator. VC081A is more simple and only learns one profile at a time. That should do for the simple use cases.