nnnup.
Clarence,
I presented my Aussie ATPL to the FAA at Oshkosh last year and I now have a FAA PPL Airman Certificate endorsed with
"Airplane Single & Multiengine Land
Issued on basis of and valid only when accompanied by Australia pilot licence number(s) 5xxxxx. All limitations and restrictions on the Australia Licence apply"
If you want CPL and ATPL you will need to do the appropriate theory and practical tests.
I would have thought the Sim ride for the 737 endorsement would qualify as an FAA ATPL check ride, if you had completed the FAA theory exam.