Or do what the Yanks used to do (probably still do) and endorse the licence 'not valid for employment within the USA or its territories'
Mach E,
That only applies to somebody who wants a CPL/ATR in exchange for an existing license.
There is no restriction on any pilot sitting the US exams, getting a medical, and doing a flight test, all relatively easy in the US, and you have an FAA license with no FAA restriction.
The only proviso is you must meet Homeland Security visa requirement, which will not be a problem if you have no criminal record.
Tootle pip!!