We took 2 weeks to go up the Trace last fall. Mostly stayed at Mississippi and Tennessee State Parks along the way so that we could have W/E hookups. I am not sure if it is a private park or not but one place we stayed at was
Grand Gulf Military Park, Ft Gibson, MS. If you like Civil War history, you should love this park. It has a small but great museum and interesting history. Would highly recommend it. The CG was as good as any of the state parks we stayed at on this trip. A little off the Trace but to us well worth it.