It's all very well coming off shift in the morning and setting out then BUT if you go eastabout most of the flights leave Europe in the evening just as you start to wake up again! Yes, you can get a flight from Aberdeen to Dubai via Frankurt (wake up to change) just after 0900 but that gets to Dubai just before Midnight (you're waking up) and the flight to Auckland leaves at 1010 next morning and is overnight to Auckland with 1 en route stop and while part of that flight might be when you want to sleep it won't be all the way and you will probably be out of synch with many other pax and the meal service.
I don't always sleep on daytime flights in business but I'm sometimes surprised how much sleep I do manage to get when I'm supposed to be awake. For example this summer on BA LHR/SEA I got several hours.
So, in the end, I'm not sure the idea is going to do much good. I'd just buy whatever flights you fancy and sleep as mauch as you can whenever you can. Me, I'd still go with ANZ.