Sorry to hear you got the run around.
I had something like this happen to me many years ago, however it happened at 6PM and I was able to resolve it and get on a flight by 10PM.
Now when AA cancels a flight and books me on another airline, I demand from the AA gate agent that she print a flight coupon showing payment to the other airline.
Last May I had a flight from YUL to ORD cancelled, I had a connecting flight at ORD to DFW and AA put me on Air Canada to ORD. I made sure the flight coupon showing payment was attached to the boarding pass.
Its crappy experiences like this that alert you to ensuring it never happens again.