If you can't add any more days, the only way to fit in Punakaiki is at the expense of half a day in FJG, but also males sense to reorganise Lake Matheson as well:
Day 9: Chch to Punakaiki
Day 10: AM Punakaiki to FJG; PM Heli-Hike FJ; stay over in FJ
Day 11: Early AM Lake Matheson; Drive to Wanaka


Not without spending all day in the car and sacrificing a lot of enroute sightseeing.
Chch to Arthurs Pass can be done in 2 hr, but you might want to stop for 30 min or longer to scramble around the limestone boulders at Kura Tawhiti. Then there's 1 hr to walk to the Devils Punchbowl waterfall & a bit of lunch (4hr).
Add 2 hr to Punakaiki and an hour to walk around the rocks (no chance to wait for high tide) = 7 hr; then a 4 hr drive to FJG.
So you could do it in around 11 hours if you don't muck about - but this is not a recommended way to travel in NZ. None of the roads are freeways or divided highways. There are multiple one lane bridges, 2 alpine passes and tonnes of amazing photo opportunities.
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