Well, unfortunately it turned out to be worse than thought. I'm sitting at the F check-in and now have to wait until they open the flight at -3h. I've read through the thread mentioned above and it appeared that they are able to check you in at -4h sometimes even earlier...but apparently not to AKL...or at least not if they don't want to

So, here's a lesson learnt and probably means we have to tag on a domestic flight next time we really want to enjoy the F lounge. I'm sure by the time we get through immigration there won't be any spa appointment left...happened to me just 2 weeks ago where I had 2 hours in the lounge.