For Australia the solution should be indeed changing the adress to a US one. To do this call US preferred hotline.
Once accomplished, you can ask them about Avis First, eventually they will let you in, considering the past rentals.
Yes, its possible to have them asign / or keep asigned the Amex AWD.

In Europe, each Avis national management decides to take place in Avis First ornoit. In Germany, since a short while they do.