I mean, good on you for being proactive. But you might as well park it in a HYSA and earn a couple grand while AA realizes its error. (I suppose they could argue that you held it for their benefit but my hunch is they would be grateful to get the money back at all!)

ETA: Never mind. I get it. You didn't get cash, you got an Amex refund. And you don't want to both lose the points (that you shouldn't have to lose anyhow) and somehow be issued a check for the negative balance that you didn't want to have, only to have to pay AA back in cash rather than on your card.

That's actually a pretty wild situation.