If you want to use the airbucks & NZ u/g your only choice is NZ via HKG. With that low amount of airbucks you'd be looking at economy fare and upgrade for one person (comp u/g to premium economy & airbucks to business on standby). Then try redeem SQ on the same flights.

Rather inefficient though. You could do paid fare AKL-TPE (not sure which airline NZ uses HKG-TPE) or just AKL-HKG. On SQ award you will need to buy HKG-TPE seperately unless TG still flies the route.