Flying SYD-AKL in Air NZ economy on a domestic A320 with Star Alliance Gold status.

Flying SYD-AKL on NZ metal in Y on a dom A320, have *G status. Is it possible to access the SQ lounge?

Yes you will beacuse you have Star Gold Status.

Yes, technically. Although the SQ lounge dragons are known to be quite protective of their lounges. It has not been unheard of for SQ to turn away *G passengers who are not flying under a 'SQ' flight number or on SQ metal. Good luck as the current NZ lounge is (being polite) well worn (a new lounge is in the development/outfitting process).

When I fly UA (not by my choice) the lounge dragons have always been nice to me letting me in the SQ lounge. 

Print out the Star Alliance lounge rules and you will be able to out-rulebook the SQ lounge dragons.