To the OP....You can apply for a Florida non-resident carry permit. Even as a non-resident, that permit will be honored in most States, including Utah and Idaho. Here is their website:
Florida carry permitNote that if you are ex-military, all you have to do is submit a copy of your DD214. You will need a fingerprint card that can be obtained at most law enforcement offices, for a charge. For awhile after the shooting at the military recruiting office, Florida had said that they would approve any carry permits for ex-military in about 2 weeks. I don't know if that is still true or not.
In any case, if you get a Florida permit, it is good for 7 years.