9 Day Itinerary w/ Fly Fishing in Mind

My wife and I are flying into Auckland on Feb. 15 and flying out of Auckland on Feb. 24. This is our first time to visit NZ. We are just in the beginning stages of trip planning and looking for some suggestions. We are leaning towards taking a flight to the south island on Feb. 16 and spending most of the trip exploring the south island because of the alpine opportunities there, although we are open to staying on the north island as well. Most of the time we want to spend tramping areas that have high alpine views and opportunities to pursue trout on the fly. Any suggested routes for tramping? We are experienced in the backcountry of the western US and can comfortably cover up to 20km per day. I've read some sites about the Great Walks. Although they are no doubt stunning, I'm not sure those are going to be a good fit for us. I'm concerned about getting reservations in the various huts and we're not really keen on overly populated areas while tramping. My understanding is that there are a lot of 3 or 4 day lesser-traveled tramping routes. If so, we would be open to two such routes with a night spent in a south island community sandwiched in between. Any specific suggestions or sites for research are greatly appreciated! We are just in the very beginning stages of planning (airline tickets were just booked yesterday). It's hard not to feel overwhelmed as it seems like we could spend a decade in NZ and not cover all of the tramping routes! So, any specifics to help us narrow our focus would be greatly appreciated. Thanks!