Most schools in Florida do offer JAA licences but I recommend at least doing a few hours in England first.
Its hard work and a lot to take in at first.
Ok, so if your going to be going abroad you wont be working full time too but might be worth getting a feel for things first.
Also, you're unlikely to pass everything in 21 days
If you do try some flying here, have you thought of schools in Barton or Hawarden?