Thanks! We don't mind paying for the AS flight to the gateway city ( can use our companion certificate). So I will only be looking for award seats of the long flight from the gateway (LAX, DFW, MIA) to SCL and back from EZE. Hoping that simplifies things.

So you have noticed the paucity of LAN award seats as well?

I guess we could fly AA; one benefit of that is their flights do not stop in LIM on the way like most of the LAN flights. But for some (probably irrational) reason we are hoping to fly LAN----if we can find the seats.