Your FAA CFI ticket (should you do that route) would need to be converted when you came back to JAA land. I know its not the full course, but not sure what the conversion criteria are.
May I ask what you've based your selection criteria for JAA schools on?
I'd seriously consider The Pilot Centre at Denham,
Welcome to The Pilot Centre, with Eva and Ian. Top rate school. Halfway between Wycombe and Stapleford with good public transport links.
Pricing is very competitive as well.
You know it!
Horst