Bienvenido, firstly.

At JFK, you’ll have to process Immigration, reviver your checked baggage, proceed through Customs, turn your baggage in at the counter just beyond Custims. Now, you are landside, so you will have to process TSA security and proceed to your gate. Officially, the IATA MCT is 1:15, and you might make it - but you’ll have to be quick. At least in Business you’ll be off the aircraft early.

Without Global Entry or e-passport, and without TSA PreCheck, it can be slow. Though AA will put you on the next MIA flight with available seats, you are quite correct that this is a high demand time of year and its (in my opinion) doubtful AA will have its grounded Boeing 737 MAX aircraft in operation. Nonetheless, they will seek to accommodate you.

Unfortunately, in my experience both AA and Iberia have untrained or even uncaring personnel among their staff; its an accepted norm here we will quite possibly have to hang up and call again. I’m sorry you’ve experienced that as well.

An agent will probably greet passengers on arrival if the flight is delayed with the express cards, so look for that agent.

¡Buen viaje!