It is very likely that QF will offer nothing in any class by mid-Dec. The only seat I found was 02 Dec from BNE. Don't know about HA - you would need to call AA.

Using CX or MH you will need two awards - one NZ to SE Asia and another from there to the USA. Again HA has some "strange" routings from Asia via HNL but might combine with MH (which now only flies as far as NRT). Availability seems reasonable from HKG to LAX with CX/AA for most of Dec in Y.

Another option might be to use the NZ$ exchange rate to purchase a ticket into Asia or Hawaii from NZ though QF's fare goes up after 05 Dec, CX on 10 Dec. Both QF and CX are well in excess of NZ$1100 one way. Perhaps a splurge on CX in premium Y?

Good luck and happy wandering

Fred