Your question asks effectively where you can purchase BTC via EFT payment from your Australian bank account.
By the sound of it, the exchanges that you have tried have made the presumptions that will prevent this. I wonder what would happen if you used a VPN to setup your account on an exchange?
There are many VPN’s available that let you specify the target exit country (Hola for Chrome for example) – it would be a fairly simple matter to trial.
It may also help if you had an Australian email address, although Gmail and similar are country-generic enough that it shouldn’t matter. Using the VPN you could probably signup for a yahoo.com.au email address or similar from your preferred webmail provider. Australian companies like iinet and Bigpond also offer email hosting.
If you were to visit Australia, it would be a simple matter to purchase from bitcoin.com.au who require minimal account setup but, a cash deposit (no EFT).
Also, you could ask your Australian bank to issue you with a Debit Card (Visa/MC logo) which will draw directly on your funds, use that for purchase worldwide.