I'm atheist & I could never make the "spiritual" side of the 12-Step fellowships work for me. I did, however, find some meetings useful in early recovery - I think the support of others with similar problems is helpful even if you aren't following the program - take what you need & leave the rest. as kevlarsjal2 says above, Tradition Three is your friend here
for what it's worth, I found NA/CA to be more inclusive of substances/behaviours other than alcohol & more tolerant of people following a slightly different path.
saying that, it can be like trying to fit a square peg in a round hole. are there any secular recovery organisations in NZ? LifeRing, SOS, SMART, etc? I believe NZ is about as irreligious as the UK, so I would expect there would be.
if not, it looks like SMART Australia do online meetings which might be worth trying if AA still isn't working for you:
https://smartrecoveryaustralia.com.au/online-meetings/