Getting your UK licence back is quite simple, obtain a medical as you suggest. Pass a Skill Test with a JAA examiner, plenty in Florida, this may require a bit of dual training as you suggest, thats it then send the paperwork to Gatwick for reissue of your SEP aircraft rating (assuming it has expired by more than 5 years.)
Popping into the FISDO is not quite that simple as you now have to get the CAA to verify your UK licence before the FAA will issue you with a Restricted Pilot Certificate
http://www.caa.co.uk/docs/33/FORSRG1160.PDF