Update
Playing around on the ANA, I found two J on NZ and return -- both on the dates we preferred. Last night and the night before the search outcome was nada, zilch.
Called CO Elite Desk to snag the flights -- Co.com, didn't list anything but Y:
First Call:
Mr. XXXX, we don't show any availability for your flight segments mentioned, not even Y.
Second Call:
Mr. XXXX, sorry you can't book NZ since the flight segments you're looking at are a UA Codeshare.
Third Call:
Mr. XXXX, our international partner desk handles this type of request, but, but, she transfers me to the Qantas, EVA, RTW Desk.
Breathe, Breathe, time for a Scotch.
Fourth Call:
Sounded like she was having a bad day, counting the seconds for my fifth call, but she was able to book my flights -- now just have to wait for NZ to confirm.
-Jim