update and thanks to all for assistance
So ... first a big thank you and ^ to FT for making me aware that I might not be able to check my bags through because of AAs policies, that had simply never crossed my mind as a possibility.
This I think either means stay beside the airport (in what look like some pretty awful hotels even for the 'airport hotel' market) or get an UberXL/Lyft adding $200 + to the cost of our overnight.
Are any of the SPG/Marriott hotels with a JFK airport shuttle tolerable?