Here are my NZ travel experiences. I always have a campervan. Saves money and time. If you don't have a campervan you'll have less flexibility. But it's not a lifestyle for everyone... and if you don't like camping, don't bother.

The objective of my trips is fishing and hiking and mountaineering. I usually spend at least 5 hours a day doing one or more of those things.

Trip 1: 9 days. Basically covered AKL to Napier/Hastings and back. Felt rushed at the end, had to drive 6 hours the final day to reach AKL for the flight the next morning. Don't remember how many km I drove, 1800 maybe.

Trip 2: 12 days. Covered from CHC to Westport to Haast to ZQN to Milford Sound and back to CHC. Felt less rushed, but still drove a lot...a couple hours a day on average...some days up to 5 hours of driving. Total of 3200km of driving. I would have liked more time out of the car.

Trip 3: 10 days. Drove from CHC to Arthur's Pass to Murchison to Nelson to Abel Tasman NP and then back to CHC via Lewis Pass. Felt rushed at times. Drove an average of 90-120 mins a day. Some days up to 3 hours. Total of ~2000km driving.

So here's my take. With 10 days on the South Island, if you don't want to be driving constantly, you should choose a section and be thorough about it, particularly if you want time to fish/hike/do tours/etc...now, if you never intend to be able to go back, fly directly into ZQN and spend all your time on the south half of the island. It's the most scenic and flying into ZQN vs. CHC will save you a lot of time. You could also fly into ZQN and out of IVC or DUD, for example.

14 days gives you more flexibility. The route I took on Trip 2 was very wonderful with lots to see along the way and 15-17 days would've been a perfect pace for that trip.

Driving the North Island end to end will take you at least 7 hours I think, and the ferry ride is 4 hours or so. If you want to see the whole of the North Island by taking that path you should figure at least 3 full days en route N to S then a day to take the ferry. Will chew up a lot of time, but the North Island is charming in its own way.