How long is your connection in AKL before proceeding to APW?

What you need to ask is for the checkin agent to ‘short check’ your bags to AKL. You might need to give a reason (going airside, seeing friends and need to get their gift from bags).

Staff at LAX may be reluctant to short-check your bags for a range of reasons.

You’ll also need the various docs to be able to enter NZ, and enough time to collect bags, store them and check back in.

Others may have more definitive advice.