I too would vote for Air NZ. I fly between the UK and NZ frequently, and having tried various options now don't really consider anyone else. I personally find straight through with no layover suits me, I find laying over just prolongs the agony, but I think it depends on your own personal preference. For the OP, trying to take advantage of effectively already being on a different time zone, I would have thought that a layover would make things worse.
PAXBboy
As to the HK / LAX dilemma, it's certainly true that HK is a far nicer transit stop, although LAX is much improved to what it once was. You have to get off the plane come what may. If you go biz, at LAX you have the choice of clearing full immigration and going to the biz lounge, or you can go into the transit lounge / cattle pen. I did the latter for the first time this year, and it was better than I had feared, with comfy seats, internet access and some food and drink available. Having said that, transiting at LA is never going to be a relaxing, life-enhancing experience.
If you're thinking of going PE, though, then Air NZ via LAX is in my opinion absolutely your best option. If you choose your flights carefully (they are only available on the 777-300), you will get their new space seats, which are fantastic, much the best PE I've come across. At the moment, they are only using them on the LAX routing, though that may change by the time you go, as I think they are rolling them out as they get more aircraft.