An update on this thread.
The EK AKL lounge is now open from 1pm. Accessed several times last year on QF ticketed EK metal in J no problem, last time in December. Knocked back yesterday 10 minutes after 1pm, flying QF in Y as QF WP (in transit from another flight hence being so early). Initial reason given was "We are expecting to be at full capacity". Then she tried to be nice and tried to get us our gate number which wasn't on the BPs. She then said (more to herself), 'now what time is the flight, oh here it is - 4pm'. At this, I chipped in - "and we will be out before you get busy". Without looking up at us, she added - "There's also the problem of consumption and catering". I was under the understanding QF would be charged for our entry.
Maybe, if seeking access to the lounge when flying non EK metal, going too close to opening times flashes a warning of - glutton, drunk, more that they could recoup from Qantas