Do you want the jet(s) on which you have experience to be included as a type rating on your FAA ATP? That will make a difference to the cheapest way to go about the process. Unlike Oz's CASA, the FAA will not transfer a foreign type rating onto an FAA licence without a flight test ('checkride' in US parlance). An approved sim is acceptable.
If so then do a type rating with the extra ATP items at one of the many sim. centres ie Flight Safety, Simcom, Simuflite etc.
If not then just about any school with access to an ATP checkairman can do it in any aircraft you like. I originally did mine in a BE76 Duchess to get one valid for multi-engine land aircraft, then years later did the test again in a C180 amphib to get an FAA ATP valid for Single Engine Land and for Single Engine Sea.
No matter which way you do it, you'll need to jump through the idiotic Homeland Insecurity/Thousands Standing Around hoops. You'll also have to do the FAA ATP theory exam. Don't worry about the exam - it's easy.
Do a search on this site for more information.