National Park Service shows three "J. Graydon"s":
Graydon, J.C.
Confederate Cavalry 6th Regiment, Alabama Cavalry
This unit served in Alabama, Mississippi, Louisiana, and Florida but not in Virginia.
Graydon, John D.
Confederate Infantry 57th Regiment, Georgia Infantry
Graydon, John G.
Confederate Infantry 57th Regiment, Georgia Infantry
The two listed as John D or John G are the same person.
The 57th saw action in Mississippi, Georgia and during Sherman's March to the sea, but none in Virginia.