I am rushing to get a LONE5 before the new 16-segment rule takes effect on 1 June. Since I will be in MEL and AKL in the coming month, which would be a cheaper place to get a ticket?

The oneworld website lists ex-New Zealand as being cheaper than ex-Australia, but this is before taxes and surcharges. Although most postings in this forum recommend getting it ticketed from AA, I understand that the AKL office has closed (I actually prefer buying in NZ). Is there an AA office in MEL or anywhere else in Australia? If this is not possible or convenient, which airline, from your experience, charges the least surcharges for LONEx: QF or CX?

Thanks in advance.