You can add 2 segments in North America but your trip ends when returning to origin. Limit is 20 segments and you have 16. You could return LHR-LAX-MIA-somewhere near ATL and then fly MIA-CUN-MIA for Christmas in Cancun, for example. Lots of possibilities, just remember your RTW ends when you reach your city of origin. If you don't need to be in AKL (and it is viable to skip it) you can fly SYD-CHC-ZQN-CHC-SYD to save a segment. Be sure to visit Milford Sound if you have the time (and Arrowtown, about 30 miles from Queenstown and much neater).