This seems like a nightmare overall...hopefully when it's all finished AA sends 10-20k miles for your trouble at least. Your time spent worrying or trying to fix their error is worth something.

It seems impossible to resolve this with AA directly as there's no customer service number and it's too bizarre to handle with an average phone agent. Maybe I'd ask the AC for help the next time I'm traveling through one, with the hope they can try to find a real person to escalate it to and the in-person conversation helps convey the issue.

Also, perhaps write a message to AMEX that the refund is incorrect and maybe they can work with AA. I imagine when they see your credit card history it's obvious it's a big error. Would be interesting if they can do like a "chargeback" on it, so at least your points are not unusable until it's fixed.