well what is JAA training then? Probably an FAA instructor doing his normal FAA syllabus. Is your licence Swedish? Then check with your CAA, but generally, you do the licence under one jurisdiction (ATPL theory and CPL), then you can add ratings as you like under other JAA jurisdictions.
The night qualification is just that, not even a rating, so even FAA is fine. The ME or any type rating can be done anywhere worldwide, some CAAs insist on you doing the JAA IR in their airspace only, but many countries take a flexible view on this...
good luck! IP