I have jsut found out that Eliz. Dun's Uncle, Walter G. Dun had a large plantation in Kentucky in after 1816. Eliz.'s father John G. Dun was, I believe, the first to import short-horn cattle into the USA & he sent them to this plantation. Would it be likely that Chas. A. I was in the Kentucky regiment during the Civil War due to this connection (Walter G. Dun would be his brother S.W. II's wife's Uncle) (A little confused; but possible?)
Also, found that John G. Dun was in the smelting business for awhile in Ohio. Perhaps that is why S.W.K. II goes out to Ohio (his father S.W.K.I was in the foundry business in Maine & R.I.)
You said that you thought there was a Kilvert fighting on the Confederate side & one on the Union side. Who fought where? That might help.