For fun I scoped out a few other routes. Lots on QF. Didn't check availability on all of them.
QF flight network: https://www.qantas.com/au/en/qantas-...t-network.html

JFK > AKL (lots of availability)
AKL > PPT (doesn't really count because it's on Air Tahiti Nui TN and doesn't seem easy to get other places I want to go from there)
AKL > SYD

SYD > BKK
SYD > DPS
SYD > HKG

Wondering how I could fit Christchurch (CHC) in, for the South Island of NZ rather than AKL on the North Island.