1) Florida only reciprocates. Since NY does not honor FL, FL will not honor NY. Recently FL dropped NV because NV stopped honoring FL permits
2) Florida only honors "Resident" permits, which I think is ironic since Florida perhaps issues more non-resident permits and any other state.
Your UT (NR) is valid in PA, VA, NC, & GA. You can carry a loaded piece in a car in SC, but it must be in the Glove Compartment.
Don't know when your trip is planned for, but if you frequently come to FL, consider getting a FL CWFL.