Far stretch if you don't go all the way around the globe. I think your best bet will be something like the below, at least the long flights are covered..
mel-doh-fco-doh-akl-scl-syd-mel
-Melb to Europe via DOH
-Get surface flights around
-Head back to Auckland via doh
-Get a short flight to Melb
-then you take off again from akl to SCL on second trip.
This is one way. I'm sure others will have another.
Edited.
