You had good luck getting a knowledgeable agent
No Oneworld airline fly LAX-SCL non stop [reference wikipedia]. You must list and count all OW flights/airports
https://en.wikipedia.org/wiki/Arturo...tional_Airport
LATAM is no longer part of OW. A big loss to Oneworld *ONE* tickets
Adding SCL is another continent, at a cost increase
Going to SYD twice is a waste. Looked at BNE for the second east coast airport (SYD-ADL-PER-BNE-AKL)? [have not checked QF time table]. But QF do operate a wide body B787 on the SYD-PER-FCO route and MEL-PER-LHR route. Far better business class seat than on the B737.
A map from the Great Circle Mapper - Great Circle Mapper