Diana --
Cloyd's company would have served with his regiment rather than being detached, so that should make your search easier. A list of assignments and actions are listed here --
http://www.civilwararchive.com/Unreghst/unkycav.htm
As you will see, the regiment served with the XXIII Army Corps rather than the XIII Army Corps. It appears that David Cloyd served with the regiment until mustered out on Dec. 31, 1864. Copies of his military service file are available here --