Sea Buck, take a look at Three Lakes WMA and Bull Creek. I am very familiar with Bull Creek, and a little familiar with Three Lakes. Both used to hold good populations of Turkeys.
As for Hogs, check out the hunting regs for Florida's WMAs. I understand they changed within the last few years and may be more restrictive as to when you can hunt. On most WMAs, you could only hunt hogs during deer season. If either Bull Creek or Three Lakes will work for you, let me know and I'll talk you onto a couple places to try.
If you were there in the fall, quota hunts would be available for rifle, muzzleloader, and bow, but January knocks you out of those options.
If you are looking for guided hunts, I watched a Babe Winkleman episode where they were hunting hogs with kids through Osceola Outfitters. They seemed like a good organization, and are located just east of Bull Creek.
You are a little further West of where I used to run around. I was in Indian River county, but ran around Brevard, Okeechobee, and St Lucie counties a lot.
Good leases in Florida are big $$$. Just warning you!
As for gaining access to private land, I can PM you with my thoughts.