I arrived in AKL the day prior to sbiddle on NZ104 (so around 5pm. Same process with just carry-on: turned left into teh Green lane but no other pax as I'd power-walked and had my yellow EL sticker.
At the next point, the I again went Green, but of course this merged with the Red line folks at the check/wait point before being directed to an agent.

I guess if the Red lane was very full then it is at that point that you possibly could have saved some time in getting to the check/wait point. After that, if no xray or physical check, then just teh walk out in single file so teh beagle can do its job.