Look at the bright side: If your AA flight is substantially delayed, problem solved!

While no one can guarantee that a thief would not take your checked bag as it goes around the baggage carousel, I note that lots of bags can arrive before the passenger does. Years ago, I had an award ticket on a late afternoon JFK-LAX flight. I got to the airport several hours early, hoping to get on the Noon departure. I did not; instead I made the mid-afternoon departure. When I arrived LAX, my checked bag was not on the carousel, so I went to the AA Baggage Office to inquire. My checked bag was already there: it made the Noon flight, even though I did not. I imagine that this also happens with some frequency to those non-revs who check baggage.

I think that there is still baggage storage available at JFK T1 and T4:

https://www.jfkbagstorage.com/