Great Walks + X in 112 days?

Hi together, I'm very glad about this website. It's great and very informative and I appreciate most of your comments. I'm a german guy 33 and not have not so much experience in tramping. In the end of this year I'm going to NZ and planning to do some walks for 3 and 1/2 month (112 days without flight). My first idea was to go the Te Araroa. But I think less than 4 month is impossible for me, so I made up my mind and thought about going the Great Walks and some "smaller" ones. I assume that I'm going with public transport from walk to walk, probably nakedbus or intercity. In detail it's Cape Reinga Coastal Walkway, Lake Waikaremoana, Tongariro, Whanganui, Around Mount Egmont, Queen Charlotte, Abel Tasman, Heaphy, Harpers and Arthurs Pass, Routeburn, Kepler, Milford Track, Breast Hill, Rees Dart, Dusky, North West Circuit (Stuart Island). While planning this trip there came up some questions. Maybe one or some of you could get me some hints. 1) Do you think it's realistic to do that in 3 1/2 month in consideration of taking public transport? 2) Is it maybe faster to hitchhike between the tracks? 3) Would you also chose this tracks or do I forget any essential walks? Can I throw any walk out of my list because of similarity to another walk? 4) For which of this walks (especially the great ones) is it recommended to book before and how long before should I book it? 5) Are there better ways to go than by public transport and shuttle services? Renting a car is not that cheap for such a long time and brings sometimes problems with it e.g. with No-Curcuit-Tracks. Thanks a lot in advance and best greets alex