Unfortunately the Canterbury doesn't have the damage control of a warship, she was built to commercial standards... The same applies to all of the Project Protector vessels... None of the Project Protector vessels were designed as warships... It would be a large mistake to place warship weapons on commercially designed ships. As much so as the British placing battle cruisers into battle groups facing battleships. HMS Hood is a great example, a battle cruiser with battleship weapons which blew up facing a battleship.... At least HMS Hood was a warship, just poorly armored... Now you wish to repeat this same colossal mistake with commercial shipping....
The British were successful using commercial ships without much weaponry in the Falklands with Canberra, Norland, and others. Much of the Pacific is without a serious air threat similar to Argentina. While the British may not have won air superiority, they were operating at the extreme range of Argentine aircraft. And I doubt seriously the Canterbury would be used in a landing operation with a serious air threat without allied air forces winning air superiority first...
Frankly, New Zealand doesn't have the forces to mount a serious opposed landing against a nation with a serious air threat alone... New Zealand doesn't even have an air combat force... And surely, the US wouldn't proceed with a landing without winning air superiority first anyway, much less the Australians...
Having said that, a Phalanx CIWS could be transferred to the Canterbury at short notice, probably mounted on the stern flight deck to provide a good ring of fire. I don't see any other realistic air defense improvements to the Canterbury...