I believe you are correct! CPT Cotter details the day's battles and losses pretty specifically. Of course, I have no "proof" Edwards was the man...but he was the only man wounded severely in the hand and the regimental losses are presented by name, company, rank, and wound. Neither Edwards or Carlile appear again, so presume they both died of their wounds. See OR Vol XX pt 1 pg 953-54. It details it all.
On separate note, not sure if I ever told you, we did place VA headstone for CPT Richard Hammond in Overall-McCulloch cemetery there in Murfreesboro. Want to get one for CPT Thomas as well since they are buried in the same grave wrapped in the same blanket.