Look like you have done research on awards to Aust/NZ. ^
A lot more than most, who post they have xx MR/UR/TYP points and need to go first class next month (maybe a little exaggeration, but not a lot)

USA to Aust/NZ there are few airlines. So matter which ffp you put the cc points into you will end up on the same airlines/alliance.
Award availability in nominally the same for all airlines in an alliance, (but can vary).
Doing one way awards will give more options. And on different alliances.
USA to Aust/NZ premium cabin awards are hard to get. Christmas- New Year is peak of peak for travel. Around Easter is a close second for award demand,
Going via Asia will be 2 awards with most(all?) ffp’s.
Some ffp's have high cash award surcharges. Real taxes are all the same
Flights (~3:25hr) to/from Australia New Zealand are frequent, to/from many cities and not that expensive.

Award cost(ff miles/points) assistance tools (use at your own risk. May not be up to date. These are not recommendations)
- AwardAce: Compare Award Redemptions Across Airlines In Seconds -->http://www.awardace.com/
- Economical Excursionist's Tools to compare Frequent Flyer Mile Redemptions --> http://www.flyermiler.com/
- http://www.flyertalk.com/forum/trave...ast-miles.html --> http://www.awardhacker.com/


Airlines that fly USA/Canada to/from Australia (not from all airports to all airports)
- United UA (LAX SFO – SYD MEL) [Star Alliance]
- American Airlines AA (LAX - SYD) [OneWorld Alliance] (AS partner)
- Qantas QF (LAX SFO JFK DFW HNL YVR*– SYD BNE MEL) [OneWorld Alliance] (AS partner) {* seasonal}
- Jetstar JQ (HNL – SYD BNE)
- Delta DL (LAX – SYD) (VA & AS partner) [Skyteam Alliance]
- Virgin Australia VA (LAX – SYD BNE) (DL partner)
- Hawaiian HA (HNL – SYD BNE via Hawaii) (AA & VA partner)
- Air New Zealand NZ (LAX SFO IAH YVR via AKL) [Star Alliance]
- Fiji Airways FJ (LAX via Fiji) (QF, AA & AS partner)
- Air Tahiti Nui TN (LAX last segments on codeshares) (AA & DL partner)
- Air Canada AC (YYR – SYD, BNE from Jun 2016) [Star Alliance]
And others via Asia & Middle East


Airlines that fly USA/Canada to/from New Zealand are (not from all airports to all airports)
- Qantas QF (via SYD BNE & MEL) [OneWorld Alliance] (AS partner)
- American Airlines AA (LAX - AKL) from 23 June 2016 [OneWorld Alliance] (AS partner)
- Virgin Australia VA (via BNE & SYD) (DL partner)
- United UA (SFO - AKL) from July 2016
- Hawaiian HA (HNL-AKL)(AA & VA partner)
- Air New Zealand NZ (LAX SFO IAH YVR- AKL)[Star Alliance]
- Fiji Airways FJ, (via Fiji) (QF AA & AS partner)
- Air Tahiti Nui TN (via Tahiti -AKL) (AA & DL partner)
And others via Asia & Middle East