I completely agree that award, premium class, direct routing between the US-NZ or NZ-SCL are very hard to get. But, the OP will be fine - as I previously stated - if they are flexible in their routiing and are persistent.
Even indirect award can be almost impossible. For US-NZ the only indirect routings are via Australia on QF, or via NAN on FJ or PPT on TN. These are all routes where premium awards also very hard. As for NZ-SCL there is no indirect routing other than through USA, which again hardly easy to get premium awards on.