How I can find classic awards easily if I don't care about the dates?

I am trying to search classic award flight. When I came to second screen where you can see if seats available I can see seats available for certain dated (still means nothing because business “availability” often means only SYD-MEL and not international leg and that will be visible only on next screen). However when I click on them next screen came and says that that there are no seats at all on that day!

In general – how I can find classic award (or any other type of seats for this merit) easy enough especially if I do not care much about dates?

Call them up on Skype?

I can use phone to call them, but this is not the point. I try to make complicated money/points booking using money not with Qantas – so I need to see availability at both places at the same time. Also they charge for booking over phone.