Have you tried booking the LAN flights through Qantas as a one world booking? This saved us heaps. Each sector is priced by mileage. It turned out to be the best decision for us.
I worked out what flights we wanted with LAN. Then I phoned Qantas and spoke to an operator. I told them I wanted to purchase a Oneworld SouthAmerica Pass and gave them the details of each flight. They priced it for me, I confirmed it and they went ahead and booked it. All done over the phone and then the itinerary was emailed to me.
The operator did tell me they do not sell many of these because not many people know about them. Booking through Qantas directly gave us a safety net so if things went wrong they would sort it out. As it was it all went very smoothly and we had a great trip.
It might be worth your while investigating if this would be of use to you. Otherwise I would book directly with LAN.