It's EASA now, not JAA. You'll also need to convert to an EASA part FCL licence, which means you'll also have to prove you can speak English...
Yes, after seven years the ATPL exams drop off the face of the Earth and back to ground school we go...
The cheapest way may be a flight around the patch in a Duchess/Seneca or the like, unless you can get the T7 on your licence at a reasonable cost.