I can answer this question from a constitutional perspective. Unemployment compensation is generally recognized as constituting a federally-granted privilege. Even as a non-resident, the State of Florida is unable to discriminate against you because of your non-residency. There are two cases that support such an interpretation -- Shapiro v. Thompson (1969), and Saenz v. Roe (1995/6). The State of Florida cannot discriminate in favor of residents or non-residents.
I hope this helps a bit. Good luck.