By doing some experimenting with a copy of the reservation I found that the problem was that one of the DL-coded flights is AS-operated.

I can add my OK ff with no problem to the booking after all the flights have been booked. The problem starts when I insert the DL ff and then remove it again. Now every time I insert the OK ff I get the NOAGREEMENT-error.

However, if I remove the AS-operated flight everything works fine. Everything is still fine even if I remove the AS-operated flight, insert the OK ff and then reinsert the AS-operated flight. Problem now is how to convince DL reservations to remove a ticketed flight and insert it again...