I do note that right around the time your man escaped, an Andrew J. Witt shows up on the rolls of the Confederate 3rd Kentucky Cavalry, which was organized in the summer of 1862. If I'm Mr. DeWitt and I escape, I'm less likely to return to northeast Missouri where they have a policy of shooting Confederates who are wandering the countryside, and more likely to return home to Kentucky.
In researching a soldier during the war, a researcher sometimes needs to use a little guesswork regarding how his name might show up on a muster list. Note that an Andrew Jackson DeWitt might be taken for Andrew J. DeWitt, Andrew J. De Witt, Andrew J. D. Witt, A.J.D. Witt, or, simply, Andrew J. Witt or A.J. Witt.... Don't know if that is what happened here, but you might order Kentucky Confederate Andrew J. Witt's military file and see if something matches up.
Just one theory. Perhaps some of the other members of this board can come up with something more solid on him.