Hobagoas..
I was about to ask what time you had on heavies, but seeing as you have just sat the entire ATPL writtens, I assume you do not meet the 3000hr and requisite heavy time requirement which would make the transition to JAA quite straightforward.
Doing your IR on the A320 sim embedded within the TR I think is do-able, but isn't there still a need to perform a CPL skills test too? I know that might sound crazy if you are A320 TR'd but you might want to check.
I am off to check this out right now, so if I find the answer I will get back to you.
Finals.