The Circle A ranch has a winter work camp. I'm almost 100% sure they are ok with people just showing up. There are some shacks and stuff you can squat in. Or if you have a vehicle you can park it and stay in that.
I grew up in Florida and I agree that it sucks. There are a handful of places that are worth visiting though.
One of them is Weeki Watchee Springs in Hernando County. There is amazing canoeing, swimming, and an old 50s theme park with an underwater mermaid show. Anywhere along that river would be spectacular to camp, though. I always see manatees, otters, and gators when I go there.
The river has a very chilly constant temperature of 74.2 degrees. AND...I just learned this...The spring is the surfacing point of an underground river, which is the deepest naturally occurring spring in the United States.
So if you're in the area check it out. Just don't be a dick and fuck it up. It's a really special place.
If you're heading to Florida sometime soon, especially the Southwest parts, drop me a PM and I can tell you where there are some other great spots depending on where you are gonna be. They are few and far between, but they exist! Florida is really unique in biodiversity and landscape and it's worth checking out at some point in your life.