A friend was traveling on a CO-issued award ticket about 4 months ago that involved flying SYD-SIN on SQ. Prior to his departure, he had made some date changes.
The SQ customer service line didn't see the change and told him CO had to reissue the ticket. CO said they didn't need to do anything. Quite oddly, it was possible for him to check-in online to the correct flights.
I'm not sure how to convince COdbaUA to force through a reissue that they don't think they need to do. That said, killing off your stop in New Zealand simply because you do not want to connect in Bangkok seems a bit extreme.