Huey,
Your best bet is to get on the www and email flight schools in the LA area close to where you plan to rent. I know a number of guys who obtained a J1 visa through their flight school, this allows you to work/train as a CFI for up to 2 years although post sept 11 this may have changed somewhat. Rents in LA I don't know much about but are probably the same as any big city these days.
It used to be that one could convert a FAA licence to a CASA licence if that person had used the FAA licence to earn a living for 200 hrs. After returning to OZ, all that is required is a Air Law exam and a Flight Test. Check with CASA as this may have changed. Best of luck. M/V