For the Florida Leg, from St Augustine, you might try FL 20 to Gainesville then FL 26 to Fanning Springs. There is a good camp there, Suwanee River Bend right on the river and close to Fanning Springs SP and Manatee Springs SP is close and a better park. Then take US 19 to Perry FL and get on US 98 west which will follow the coast line all the way west in the state. In Port St Joe there is a very nice, but old park, Indian Pass RV. It is a bit off the main road but is right on miles of white sand beach.
Continue west to Pensacola when YOu will have to get on I10 for awhile. Azalea Acres In Robertsville AL near Gulf Shores is a good park. We generally take US 98 to Hattiesburg which is supposed to have a good state park, we have not used and then switch to 49 to Jackson which is just east of Vicksburg.
This is scenic but not fast once you get on US98. But it is quite scenic going thru a number of small towns. The state park at Port St Joe is still being rebuilt after storm damage.