At this point I would accept the 1 stop flight is good enough and stop spending your time trying to optimize this. It is unlikely you will succeed getting either airline (AA, BA, or DL) to put you on a different carrier at this point. If there is a direct DL flight with availability, they could try talking with Delta at the airport but that is not guaranteed to work.
I had a similar scenario happen to me. Bought a ticket on airline 1 (UA); operated by airline 2 (LH); IRROPS caused the flight to be rebooked on airline 3 (AF). I wanted a better routing but there was nothing UA and LH could do despite many hours on the phone and even conference calling the two airlines together. The ticket was paid J with 'elite' status on *A and ST.