Have you considered Emirates?
I flew them FRA-DXB-AKL last month and was impressed no end (Business, mind you, but the seamlessness of the experience was a positive)
They fly to CHC via DXB and BKK (with a change of aircraft in each case) plus a transit in SYD and appears to be significantly cheaper that their LHR-DXB-(SYD)-AKL routing.