Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
I think the key is to determine whether the availability problem is for the international leg(s), the domestic (U.S.) legs, or both. I would start by checking aa.com for availability out of DFW and LAX to MEL. If nothing, try delta.com out of LAX (Virgin Atlantic is a DL partner), and united.com out of LAX and SFO (NZ is a UA partner). If you find "Saver" seats at united.com on Star Alliance partners, you should be able to book them after transferring MR points to Aeroplan. But be aware that Aeroplan imposes surcharges on award travel on all carriers except the following:
Air China
Brussels
EVA Air
Egypt Air
Ethiopian
Scandanavian
Singapore
Swiss
Turkish
United