<<An FAA flight instructor can be signed off to teach JAA syllabus after a brief checkride (only valid while staying with that school)>>
That is not correct. Any new foreign qualified instructor wanting to teach towards a JAA licence or rating has to undergo a standardisation course as laid out in the FTO's CAA approved Ops manual. There is no laid out minimum but it has to be approved into the manual by the authority. A ballpark figure would be 15hrs flight training with 30hrs ground school. The instructor would then need to have a flight test with an examiner acceptable to the authority. This examiner need not be a FIE if only PPL instructing will be conducted. If the instructor will be conducting training towards a JAA commercial licence then the test will in all probabilty be with a CAA staff FIE.