How about EK SYD-DXB-IAH?
True, but you'd have to be a strong EK supporter to prefer this to UA's SYD-LAX-DEN-IAH which at under 22 hrs is about 10 hours quicker
In the late '70s and early '80s, Pan Am used to run PA001 and PA002 as round-the-world flights with a route approximately (scratches bonce):
JFK-LHR-FRA-THR(!)-BKK-HKG-TYO-LAX-JFK and v.v.
Sadly, I don't have my old timetables to confirm how long this all took. It's a bit of a shame NZ don't do this with NZ038 and NZ002 to produce an LHR-HKG-AKL-LAX-LHR route!
Oh, and
Flapping_Madly - at least you're not going on NZ001 via LAX which adds another couple of hours to the Auckland journey. If you've not been to NZ before, it's worth every minute of the 24hr trip!