I have been looking at doing similar. From what I can gather, anything other than a PPL is not a conversion as such, given you are still required to complete the FAA flight test for the licence. As such I suspect the currency of your Australian licence will be irrelevant, all you have to be able to do is demonstrate you meet the FAA hour requirements for the licences you are seeking. You will also need an FAA medical prior to the flight test.
However the catch is that you have to do some training for the licences, and this must be at once of the flight schools that can issue visas for international pilot training. The schools that can do this are quite limited from what I can see. At the ATP level it doesn’t seem as bad.