George, Using the Civil War Database which is a pay site and also has its problems from time to time; there were soldiers also killed on September 20, 1863 at the Battle of Chickamauga within the 7th Regiment Mississippi Infantry and both were officers. I was able to confirm their deaths on fold 3. One was Captain John Milton Brister of Company B of the 7th Regiment Mississippi Infantry. Like Richard B. Pittman I could not find anything about him on Find A Grave or the NGL; but I did not look very long on other sites.
The other was Captain G. A. Robertson of Company G of the 7th Regiment Mississippi Infantry. But he sort of has an Find A Grave Memorial at the Marietta Confederate Cemetery. He is on a plaque of Mississippi dead there. And he does have service records at fold 3.