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You don’t even need to do that. Once you have Residency (distinct from Permanent Residency and Citizenship - the one with the passport) you are allowed to start your own company which you can use to contract yourself out to Australian companies for annual amounts double those of a lot of NZ roles.

(My last role paid 240-250K NZD depending on exchange rate; the local role prior to that: 120K NZD)

Didn’t know about E3 visa route. Very interesting, thank you