As you know, Southern dead from the Chickamauga battlefield were removed to the Confederate cemetery at Marietta. The 20th century headstone in the cemetery near Clayton certainly appears to be a memorial placed by a descendant. Why would Floyd's body not be buried with other dead of the 39th Alabama at Marietta?

Battlefield markers at Chickamauga battlefield show the position of Alabama commands at different times. Using NPS battlefield markers, my wife and I followed the path of her Confederate ancestor at Chickamauga. This unforgetable experience was the result of a spur of the moment idea.

We cannot know exactly what time Floyd was killed, but Floyd's military records report his death on Sept 20th. That eliminates battle actions of Sept 19th and narrows your search considerably. Are you aware of battlefield markers for Deas's Alabama Brigade?