New Zealand is cheap for a LONE4 - NZD3799 (~AUD3170) compared to the Australian price of AUD3699
and the incremental cost of a LONE5 over a LONE4 is only NZD300 (~AUD240)
Significant savings in fuel fines can be achieved by ticketing with either LAN (e.g. start with AKL-SCL or AKL-SYD but with LAN not QF) or AA (i.e. start with AKL-LAX on the AA codeshare on QF metal). I costed up a LONE4 itinerary using the OneWorld tool starting with AKL-SCL on LAN - the total cost came to less than the base ex-Australia price
Sagy's spreadsheet is useful. It shows that New Zealand is the 3rd cheapest place for LONE4/5s and that Sth Africa is the 3rd cheapest for a DONE4 (and that Australia is the most expensive

)