Thank you all for your perspective. Our flights there and back were booked through ANZ. They include two legs on UA going over and the last leg coming home. For completists, it's CLT-ORD-LAX-AKL-CHC and TRG-AKL-IAD-CLT. I think I'll just follow Thai-Kiwi's advice and just use my ANZ account number.

As for Koru, we're on an 8 week trip with multuple flights and airports to deal with, and small amenities like preferred check in, up front seating, quicker and extra baggage, and lounge visits all add up to a smoother travel experience. I joined before the price increase, fwiw, did the math and made the decision that the value was worth the cost. YMMV.