Looks pretty ok to me.
My pack generally weighs about 25kg on the way in with 4 days food. I take pretty much the same stuff as you.
Bivvy bag isn't a necessity, but I take mine - good choice. If you are going to be in avalanche prone areas, don't do them on your solo. I cant tell from your brand of cooker, but an LPG canister wont work at tahr and chamois heights in winter without pre heating the canister, which can be a bit dangerous, and uses precious gas. I use white spirits in a primus omni fuel.
Take plenty of ammo. You are supposed to cull 3 nannies for every bull, and 5 would be better.
Best bet is to head over to Fishing and Hunting New Zealand. fishnHunt is New Zealands biggest and oldest fishing and hunting website. Home of the famous Fishnhunt New Zealand hunting and fishing forum.
and ask a few questions. Heaps of very experienced alpine hunters there.