We've had a hypothetical invasion of NZ thread before (search this thread group although it may have been merged into this topic from memory). I don't want to bring that up again because it went downhill quite quickly (and it may incur the wrath of the defpros or mods), seeing there is no definition of who the invaders are. If you mean China invading NZ, forget that, they could buy up more NZ industry, enter into more partnerships or lock in long term supply and exploration arrangments being win-win for both sides. China would have to take out most of SE Asia to get here (and if it happened, you'll see NZ Govt boosting defence preparations faster than normal etc).
A better case you could be making is to prevent a repeat Mumbai incident - that is more likely than an undefined invasion - and your scenario better fits that type of terrorism scenario, rather than an invasion from another country. Overseas troops are usually professionals working with set procedures to ensure their objectives are met eg taking over the functioning govt etc (not acquring buses with no protection and shooting their way from AK to WN Parliament). Your scenario fits an irregular warfare, fanatical or terrorism scenario IMO.
I won't say anything further on this scenario (I've responded seeing you quoted my post, which was made when the DWP came out. After 25 years of capability cuts I was pleased Govt DWP ensured no capability cuts and some growth in new areas such as C&C and ISR. Granted this is all bare minimum and still prone to allow policy failure and we know nowadays Defence has to find alot of savings from within so DWP has taken on a new meaning in light of this, but we should be grateful it wasn't alot worse).