The fact that you are flying C class would make me lean towards putting the miles with LH (as you get 200% of actual mileage in C class), and that fact that you will hit FTL (Silver) mid trip and then rake all subsequent miles in at 250% of actual mileage flown would be enough for me to put the miles on LH.

However, having said that I am slightly bias towards LH MM, so you would be well advised to hear the expert opinions on NZ and UA.

Hope this helps