At midday I had been told they were working through the bin my parcel is in and that there are only 4 staff working in international parcels so "things can take days to process".
It took me until 3:50 to get through to someone who told me that they are short-staffed and confirmed that there are only four of them. The woman I had spoken to at 2:30 only works till 3pm so wasn't even there at the time she asked me to call back.
According to the NZ Post staffer I spoke to there is only one customs officer working with them and she is only there a couple of days a week, for between 2-4 hours each time. She said customs was really short-staffed at the moment (have since learned that customs officers are away doing a boat people exercise).
So, after all these calls, I was told that I am not likely to have the notice & entry numbers before Friday at the earliest and I might not get my parcel before the end of next week. She said parcels are processed in order of arrival as much as possible.
BUT - the NZ Post tracking site has been "updated". This morning it showed all the details as above. It's now been edited to show the parcel arriving yesterday. They have changed the "Held for clearance" date to today, at 2:48pm, coincidentally, just before the woman I spoke to left for the day.
I didn't get screenshots because I didn't know I would need them. Not so sure I can trust any kind of tracking from NZ Post now.