This is what I know; a type rating in USA is now impossible until they lift the '9-11' restriction ( it is now impossible for a non American national to get a type rating and as I understand it, that also goes for a green card holder.) The outfit in Perth Australia no longer do it, Rossair don't do it either although they might if you have a South African licence... best to contact them directly.
The only other suggestion I can make is Canada...check the forum because someone mentioned a place in Toronto on one of the threads. (Once again though, I think you need a Canadian licence.)
Re the JAA thing, no idea!
Hope this helps a little.
F-S