There is no good way to avoid Nashville from where you are coming from...UNLESS you want to take secondary roads and add a bunch of time to your trip. Most secondary roads are just fine to take but the stop and go will add hours to the trip that will take 6 or more hours by interstate I'm sure....according to Google maps anyway. Bite the bullet and go straight through.
Have you been to Tims Ford before? There are 2 campgrounds, the main one and Fairview Devil's Step that is 10 miles south of the main CG. How big is your rig? The main CG sites will accommodate rigs maybe 30 ft long...and that would be tight IMO. Fairview has the larger sites that will accommodate the big rigs. My TT is 37 ft. long and Fairview is where we stay when we visit Lynchburg and the Jack Daniel Distillery. One of our favorite parks.