I'm not sure if your search included LAN.. but there are quite a few seats available on them, although via SCL. Connecting on LAN via SCL is quite different than connecting on AA via MIA.
I flew the new nonstop JFK-SCL, and it was fantastic.. I'm 6'5 and I managed to sleep quite well on their new fully flat J seat.
AA has pretty much got a strangle hold on nonstop JFK-EZE traffic, so I'd just grab the LAN seats and not hold my breath for a U seat to open up on AA.