There is generally very good availability in both Business and First on AA into all of their Asia destinations. There is also very good availability to Australia on JAL out of Narita and now also on Malaysia Airlines from Kuala Lumpur. Use the BA website to check availability. I was quite suprised how much availability in premium cabins was available if you used AA to Asia and then a One World partner from Asia to Australia. You just need to put the time into checking all days/destinations.
Disclaimer - this will require extra miles.