The good news is that you can get off Tahiti to NZ. The bad news is that it will put you over 34,000 miles on the route I proposed. It may be possible to tweak this route some or you may have to drop a segment. Probably the easiest to drop and cheapest to replace with a separate ticket is AKL-SYD instead of AKL-BNE-CNS-SYD. This will get you well under 34,000 miles so you can use a MGLOB34 ticket originating from LHR.