Check Florida State law to see if there is a preemption to allow you to possess weapons in company parking lots. A lot of states now have them for just that reason. Florida being a leader in carry laws I'd suspect there is one.
If so, the company policy is technically invalid (though it may take a court case) in any event, law or not, you don't have to tell anyone you have a gun in your car. Make sure you are responsible and get some kind of safe/lockbox so a smash and grab artist can't get your weapon. Hiding it is not a solution, they know the hiding places better than you.
Once my company came up with their policy in August '05, I had to park across the street until Alaska's law kicked in in October of that year.