in the X2Go Client that you want to connect as he second instance (equivalent to screen -x) you have to select session type "Connect to local desktop" in the session profile.
I see, that did the trick. It would be nice if, when the list of sessions comes up, this option was available right there.
In any case, this works very nicely, thank you a lot! (And I must say it feels much faster than anything I've tried so far.)