hauteboy is correct. There are plenty of M class seats from SCL-PPT on LA in January and from PPT-AKL-SYD on TN/QF in February. Remember, the SCL-PPT flights only operate on Wednesday and Sunday and the PPT-AKL flights operate on Thursday and Saturday. You cannot go directly to SYD from PPT. You must travel via AKL.

You cannot go via LAX. The route I proposed is a Global Explorer, not OWE. As I stated in that message, you cannot change any locations without giving something else up. Going via LAX would not only put you well over the 34,000 mile limit but you would not be able to stop in PPT.