The next time you're in the U.S., you can use BA miles to fly LAN to South America. Imho, LAN have the best hardproduct J cabin, specifically the seat and IFE, in OneWorld. A roundtrip from JFK to Easter Island in J, with free enroute stopovers (i.e. Santiago and Lima) costs 80k BAEC miles, minimal taxes (no fuel fines) and there's generally very good availability. The only downside is that any BAEC itinerary with stopovers requires a phone call to your local BAEC office (and associated telephone booking fees).