I don't know whether it was the time of day that I called (5 PM) or the fact that it was about two weeks before our trip, but after weeks and weeks of calling every day looking for an opening for our dates, I was finally able last week to change our ressies from AKL to YC. It had been booked solid up til then.
Every time I'd called before that and asked the CM when I'd be most likely to nab a cancellation, I got a different answer ranging from something like 21 days prior to 5 days prior.
Good luck! I bet something will turn up for your dates, too.