I am not familiar with AA policy. I have had good luck in the past with United, perhaps at least partially due to my loyalty status with them. Generally, the airline will try to re-book on their own flights, then look for joint venture flights if any, and then look for other airlines in the same alliance.
I would suggest you look at AA flights that might work better for you, or perhaps British Airways flights as an alternative. Then present these alternatives to the AA reservation agent asking for their help with your situation. It is useful to try to get the agent to be empathetic and want to help you. Getting angry will be counterproductive. If the first agent with whom you speak is not helpful, then implement the HUCA guideline = Hang Up and Call Again.