Can you get any copies of the reports by the officers? I suspect those might 1) raise the ante (after all, the agent and her accomplice twice attempted to have you falsely arrested! ) or 2) be helpful when you find the appropriate attorney. You were merely attempting to follow stated AA baggage policy by filing a claim:

"If you are unable to locate a checked bag upon arrival, you should notify an American Airlines/American Eagle baggage service agent prior to leaving the airport. At that time, you will be given a Baggage Claim ID and a brochure explaining the baggage recovery process. Please refer to your six-letter file locator in all conversation and correspondence regarding your claim."

I strongly recommend documenting as thoroughly as possible now, while it is clear in your memory - names as possible times, locations, contacts with the Plat agent, etc. etc.

The JFK bag office needs a strong purgative to fix what ails it, as CharlesMD might put it. Or not.