Jack contacted my offlist, but sharing here for completeness. I posted the photo at Find-A-Grave he mentioned. I also have a family history that contains these names. I've not done the research yet to find the evidence, though the writeup does contain references.
J M Willis could be either John Milton (father) or Joseph Merry (son). Don't know much about Joseph Merry Willis, but thinking he was killed during the war. Also John Ethelwin Willis (son) is stated to have been killed during the war, his sons being reared by his sister, Emarintha Electa (Willis) Waters.
Emarintha married William Robert Thompson Waters, your W T W no doubt. They had a daughter, Bessie Willis Waters Thornton, who left a paper "My Road To Life" in the Tulsa library. I obtained copies last summer (May 2010). It is her story, so nothing about the family during the Civil War. Her DAR app is online, and IIRC, she was a founder of the Columiba chapter.