You may try flying AA to Spain and choose long routes, such as SCL-DFW-MAD or SCL-DFW-ORD-BCN. AA is often the cheapest option from Spain to Peru and Chile (and also in the oposite direction). Be careful not to book flights in O, as they earn no kms. From Spain, you may find relatively inexpensive flights to Germany on Iberia or Air Berlin. Your trips won't be very quick in this way though.

A "good" thing about AA is that it often has schedule changes. If a change is incovenient, AA is normally happy to rebook you into a direct LA flight in Y, meaning you will earn 100% kms for such a flight.