Well the only fixed wing schools I know of in Florida and who have "JAA Career Pilot Programs" are:
http://www.flyeft.com/
http://www.naples-air-center.com/
http://www.flyoft.com/
There are probably others but I'm unable to remember who they are at the moment, apologies in advance!
I can't recommend any of the schools above in regards to the JAA CPP course as I have never attended the schools for the afformentioned course.
I am however doing my ATPLs with NAC and find them good (94.4% average with no fails in my exam results so far) as well as having done the FAA CPL/IR at NAC. So from a personal point of view I can't fault them as I have never experienced any problems and they have only been friendly towards me and plenty of other people I know. BUT on the other hand I do know someone who would say something slightly different (recent over booking in the flight department).