I wholeheartedly thank you for taking the time and the patience to call through the bluff of Christina Walker and deal professionally with the police. This type of abuse by an employee is completely unexcusable, and am sure many other passengers had been subjected to her shenanigans. As averyone knows here, if you don't get your luggage you simply don't leave the airport without a filed report.
I assume that AA fired her. If not, it's a very bad reflection on the airline.
Incidentally, I completely agree that the settlement (in vouchers, not even cash!) for being slandered to the police is completely unreasonable; I assume it doesn't even compensate you for the time lost by the incident. I hope you find a lawyer to take on this case -- for the benefit of the rest of us.