If you booked on a two-class 777 (with lie-flat J) and the equipment changed to a three-class 777 (with angle-flat J), you're entitled to change flights because AA changed the equipment.

Does flying through MIA help?

If that doesn't work, perhaps you could be rerouted through another South American city (e.g. LIM or EZE or MVD), using LA to connect to an acceptable AA flight.