I try to end up around 12 lbs per day.
You need:
Rifle+ammo
1 knife (make it count, you only need one!)
Binos and rangefinder
These items aren't included in my 12 lbs per day.
I would suffer the same clothes for the whole trip with the exception of a extra pair of socks.
Small cook stove with butane lighter, fuel, 4 mountain house meals and a water purifier bottle.
Top it off with a sleeping bag and the largest trash bag you can find and you're done. Even things like extra matches, a plate to eat off of and spotting scope and tripod are luxury items. If you want to cut down on weight you have to make sacrifices. You have to decide what YOU need. If you can make your own chopsticks to eat with or whittle a spoon, then you don't need to pack one.
I know what I absolutely must have from thousands of days of experience.
I know that I can make it without electronics like GPS and extra batteries.
I don't need to haul 10 gallons of water as long as I have available water and a filter. I don't need a tent, but I have no idea what the NZ climate is like so you may need one. Your head is in the right place though. I've hunted with lots of guys who think a backpack is an RV and a pantry rolled into one. It's called roughing it for a reason!