There is not much F (at least good F) between Asia and Australasia or between North America and Australasia, so an F award may not be great value.
SQ has mostly 77W and A380 to SYD, MEL, AKL; which are not available in first on awards unless you get very lucky.
SQ has regional F (773) on some flights to MEL, plus ADL & PER. PER is not a good idea - short flight. SIN-ADL is a short overnight flight so not a great F experience.
TG is reintroducing F on some Australia flights, but it has been pulled before so no guarantees it will stay.
Other than that the only *A F is UA (new F) to SYD & MEL.
I'd stick with NZ C, and if you can book NZ direct LHR to AKL vv then you can add another region for free (+ taxes).