There are actually a surprisingly large number of CHC-AKL 'international' flights (though not in the other direction, strangely), and the NZ90 and NZ98 connect quite well to TG AKL-SYD.

For Feb-Apr, for example, there are the following CHC-AKL flights offering C class (and, one assumes, the NZ4 and NZ 6 probably offer F as well since they connect to the America routes):
Flight Frm Departs To Arrives Typ Meal Freq Begins Until OperatedBy
NZ 90 CHC 11:00am AKL 12:20pm 744 S .TW.... 17FEB04 17MAR04
NZ 4 CHC 3:40pm AKL 5:00pm 744 S ......S 21MAR04 21MAR04
NZ 90 CHC 10:00am AKL 11:20am 744 S .TW.... 23MAR04 24MAR04
NZ 6 CHC 1:00pm AKL 2:20pm 744 S .T....S 28MAR04 16MAY04
NZ 4 CHC 3:40pm AKL 5:00pm 744 S ......S 15FEB04 07MAR04
NZ 90 CHC 9:40am AKL 11:00am 744 S ..W.... 31MAR04 28APR04
NZ 98 CHC 10:40am AKL 12:00N 744 S M....S. 14FEB04 08MAR04
NZ 98 CHC 10:40am AKL 12:00N 744 S ......S 15FEB04 07MAR04
NZ 98 CHC 9:40am AKL 11:00am 744 S M....SS 21MAR04 28MAR04
NZ 98 CHC 10:40am AKL 12:00N 744 S M....SS 13MAR04 20MAR04
NZ 98 CHC 10:05am AKL 11:25am 763 S ......S 04APR04 26SEP04
NZ 98 CHC 10:05am AKL 11:25am 763 S M...... 29MAR04 27SEP04
NZ 98 CHC 10:05am AKL 11:25am 763 S .T..... 30MAR04 28SEP04

Glad you enjoyed the trip report, by the way! I *must* get around to finishing it...