Most (maybe all) public land is closed to hog hunting unless a regular hunting season is in session. If you can gain access to private lands with hogs then you are good all year-no license required.
Go to myfwc.com for management area information.
A truly unique hunt that is not too far from Panama CIty is the St Vincent NWR hunt. It would require a little effort (draw, primitive camp), but the biggest expense is a shuttle to the island. When I hunted there we saw a lot of pigs. Google them for details.
Good luck!
Gregg