Cough up the $50 or so and take the concealed weapons course at the next gun show. Then pay the $112 for the concealed weapons permit. The license is now valid for 7 years!
790.25 Lawful Ownership, Possession, and Use of Firearms and Other Weapons
(5) Possession in Private Conveyance.--Notwithstanding subsection (2), it is lawful and is not a violation of s. 790.01 for a person 18 years of age or older to possess a concealed firearm or other weapon for self-defense or other lawful purpose within the interior of a private conveyance, without a license, if the firearm or other weapon is securely encased or is otherwise not readily accessible for immediate use. Nothing herein contained prohibits the carrying of a legal firearm other than a handgun anywhere in a private conveyance when such firearm is being carried for a lawful use. Nothing herein contained shall be construed to authorize the carrying of a concealed firearm or other weapon on the person. This subsection shall be liberally construed in favor of the lawful use, ownership, and possession of firearms and other weapons, including lawful self-defense as provided in s. 776.012.
The securely encased part usually means in the glove box or center console. I have heard some police officers say it must also be in a snapped holster or zippered bag. Nothing in the statutes quoted above indicate that. If you are legally able to get a concealed weapons permit, I strongly suggest you just go that route.