Thanks for following up with the timeline, very interesting!
For AMEX, it's weird to me that their system would ever allow this - charges and refunds happen by the millions and is basically the core-est of core functions of any bank/CC.
For AA, simply astonishing how many times they insisted there was no issue. I'd like to sit here and say that if I had told them multiple times and they insisted it was fine, in writing, then I'd have kept the money, but in reality I wouldn't be able to sleep at night if I did that.