Longline
You will first need to get an FAA CPL issued, but first you need a clearance from FAA and imigration I think, before entering the country for flight training.
Then go to the States roll up to the FAA ,they will issue a PPL H based on your CASA CPL, then sit your CPL exam and flight test and get your FAA CPL.
Then under go IFR training, do some in a fixed Wing Dual dont worry about not having a FW licence , they accept this, then sit your 1 ATP exam and flight test.
Your best bet is contact Ron Gudstafson at Avia flight Services in Corvallis Oregon , He has done dozens of Australian and NZ conversions to FAA, he is a good bloke and he will not misled you. he runs a good outfit and I am sure you will enjoy the experience.
Conversion to CASA I am not sure about but under the Kiwi system you must have gained 500 hrs on the ATPL before they will reconize it, but then again they are the NZ CAA
"C***ts Against Aviation"