I have been playing with Google maps. Here's my first thoughts for the first few days.
Day 1: Christchurch (A) to Mt. Cook (B)
Day 2: Mt. Cook (B) to Dunedin (C)
Day 3: Dunedin (C) to Milford Sound - Stay there or in Te Anau (D) or at HondaV2's Shaggy Shed!
Day 4 (or 5 if I mess about in Fjordland another day): to Franz Josef glacier Nat. Park (E)
Day 5: To Arthur's Pass - Maybe further, depending whether I spend half the day hiking on the glacier or not
Day 6: Back to the East side and then cross to the West again via Lewis Pass and Buller River Gorge