Would a travel agent be able to do it for you?
I had a similar headache a couple of weeks ago trying to route AKL-SFO-JFK vv; it kept pushing connections on DL and VX (and UA to EWR), none of which worked as my +1 was already booked separately on UA to and from JFK. In the end I had to make two separate bookings; one on NZ and one on UA (and saved $400 in the process!)