To my knowledge an ATPL national or JAA has never included an SEP ratings embedded in some other class. You have always required a certificate of validation for each class.
The only embedded privilege was on a UK licence fir the IMCr.
So I would suggest that the FAA are quite correct in refusing you.
Believe it or not button pressing an airbus for a million hours is actually a little different from a 172 and needs refreshing from time to time, sky god or not.......