Hi. I'm in the Tampa area and love flying in Florida. If the FAA says no, then you are not eligible for LSA either. See 14 CFR 61.23(c)(2),
Have been found eligible for the issuance of at least a third class airman medical certificate at the time of his or her most recent application (if the person has applied for a medical certificate);
Not have had his or her most recently issued medical certificate (if the person has held a medical certificate) suspended or revoked or most recent Authorization for a Special Issuance of a Medical Certificate withdrawn; and
Not know or have reason to know of any medical condition that would make that person unable to operate a light-sport aircraft in a safe manner.
see: Frequently Asked Questions About Sport Pilot - AOPA