We did it! After 24 hours and almost 1,200 miles in our honeymobile, we dropped the car off and headed to Kauai.
Here's a map of our journey, which we would highly recommend should you find yourself on the South Island with 12-14 days free. We can't take credit for the itinerary (thanks, TripAdvisor community!), but it was the perfect balance of adventure and relaxation.