I had a very easy time getting HKG-AKL and return as part of a OW award, with dates in early Jan. Several open days to choose from. Though this was exactly 330 days out. IME the hard part is finding the seat HKG-US though hardly impossible. I decided to route through NRT and spend a few days there on the way home. But to answer part of your question, yes, it's possible to get HKG-AKL on CX in U as I just did.