Air NZ. Only practical method for time of day practibility.
Been a while since have been, but if u want reliable the AirNZ is the way.
If You're flying on to Va'vau be accepting of "unable to land" turn arounds...very common due to local pilots being afraid to touchdown once at destination.
Also goes for Ha'api.
And also when leaving such spots.
If u get into trouble exiting the islands, (esp Va'vau) then best bet is to fly to Fiji direct (more likely to take the route than the Nukualofa route)and connect with an Air NZ out of Nadi, back to Auckland then AU.
Main reason for that is often flight back to Nukualofa are cancelled, often without refund or transfer....or recourse.
(It's the style in the islands of Tonga, hoping they have improved since my last excursion.((took me a week of flights cancelled to Nukualofa before I figured Va'vau to Fiji was more practical)) Insurance company took a lot of talking to eplain multiple cancelled flights without refunds... Might pay to research the current local inter-Island flight service if you are making it to the outer and tastier Islands .
But either way, nice place to have a problem leaving.
;-)
EDIT....POST SCRIPT.... The flight difficulty I mention are related to Island Weather conditions as far as Failure to Land instances in the satellite Islands.