May is a good month as it is the low season for travel to Oz. As BAHumbug notes, Easter is at the end of April which means that availability is going to be very tight to non-existent.

I managed to bag 2 F seats to SYD last year in May - and that was booking at the end of September so it can be done. While it is frustrating to have to avoid certain months that is the way the game is - I certainly don't believe that 2 seats are released on each flight as the award availability seems highly dynamic i.e 4 seats to EZE on one day, and nothing on the following.