LAN Airlines now flies from Sydney to Santiago, as well as from Santiago to Mexico City. ITA Matrix gives an approximate price of $2600 for a round flight through Chile.
Ok, maybe not an actual answer, but this might be another option:
An ex-coworker who used to have a boat and told me that is quite easy to get a lift on a boat or yacht from Mexico towards (south-) west; so if you’re on a budget and not in a hurry you could try to buy a one-way plane ticket to Mexico and then sail back towards NZ or AUS from Mexico. Right now i could only find this one offer, but you have better luck if you ask the locals at the marina in Mexico when you’re there…
Plus you get a chance to see all the little islands like Fiji, Cook Islands, French Polynesia etc. on the way.
The only thing I can think of is:
Credit:stackoverflow.com‘
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