My wife was on your flight and did hit a brick wall dealing with the local Korean AA Office.
She said that they had trouble speaking English and did not seem empowered to do anything other than find space for her on the next available AA Non-stop and either did not understand or were unwilling to look at other airlines.
She emailed me and I called the 800 line from the states and as you outlined the flight was not cancelled immediately in the system and the agents in the states were somewhat powerless to do anything.
However I got a really nice fellow on the phone who called ops and was able to determine that the flight was indeed cancelled, got them to do whatever was necessary to allow the agent to work on it and he rebooked her on Asiana ICN-LAX-DFW the following day.
She did miss the bus to the AA paid for hotel, but she did not care and was happy to be rebooked for the following day and she stayed at the Hyatt at the airport on her own dine.
AA to date has not offered us any miles nor reached out to us and honestly I don't think she cares, she was just happy to have it all work out.