When my Aussie medical expired (and I had an FAA cert based on my CASA license at the time), I went and got a Class 3 medical in the US and the FAA gladly accepted that on my records and allowed me to keep my license based on foreign privs.
Process for doing this with a class 3 medical:
1) Pay CASA to release your information, where you specify FAA at Oklahoma.
2) Wait 2-3 days, call CASA and check if they have sent your details to the FAA
3) Wait 4-5 days, Send form to FAA to validate your foreign license
4) Wait 10 days. Call FAA and see if they have your paperwork
5) Book AME appointment with a doc. You will need to provide an address where you can be reached in the USA. Cannot be a hotel and if the address changes, you need to notify FAA pronto.
6) Get class 3 issued
7) Go to FSDO with log book and Aussie license. Book an appointment prior. You'll get a paper license
8) Call FAA and change your address to your overseas address
9) FAA will mail out a full cert to the address on your file.