Maybe Blue Springs (right down the road from Ginnie) might be a better idea; they're generally quieter. They don't have a river run, though, just the springs proper.
Neither of those have hiking, though; they're definitely car camping sites.
For hiking and water combined, there's Ichetucknee Springs; the campground there isn't actually in the state park, it's a privately-owned one across the street. Means that you aren't actually camping on the water, but it's awfully pretty up that way. The hiking is strictly short loops, though. If memory serves, the longest one is something like two miles.
Anyway, outside of Ocala National Forest, I can't think of anywhere where there's good hiking, springs, and the ability to hang off of the top of my head. Seems like the triple crown is always hard to get a hold of, eh?