I've done the vast majority of my flying and instructing in Florida
You say you hold a JAA FI but have done instructing in Florida.
It appears you have a UK JAA FI - so therefore how have you managed to isntruct legally in Florida - as it is a requirment to have an instructor rating issued by the country you are flying in by the UK CAA to instruct in another country.
Or was that an uninentional slip?
You also require a visa - as US Immigration say that having the aircraft rental paid for by the student consitutes work - or daren't I ask that?