Conclusion
I only saw a tiny part of New Zealand - nothing of the North Island, or of the north or south or east coast of the South Island. The trip was effectively a circumnavigation of the Southern Alps. That leaves plenty for later trips, and I'm certainly coming back.
The highlights? It was all pretty amazing, but the Three Passes, Franz Joseph Glacier, and Mt Cook stand out, with the single best day being the crossing of Whitehorn pass. I like mountains, as you've probably noticed! If I did the same trip again I'd try to fit in a climb of Avalanche Peak at Arthur's Pass (a solid daytrip) and would spend two days at Mt Cook and skip Lake Tekapo.
Thanks to Joe for inspiring the trip and organising the walks, and to Adrienne for prompting me to actually go along.