Gday mate,
When you talk to CASA do not believe anything that you are told by the people that first answers the phone. I don't wish to be mean, but on many occasions they have simply given me completely the wrong answer.
Ask to be put through to the person in charge of the department or email them.
As long as you do your TR at an FAA approved center then CASA will accept it. You also need to fill out Form 209 (CASA) and they advise to provide a copy of the centers FAA approval to speed things up.
They advised me that it would take about 2 weeks to process.
Good luck
JAB