I wrote about the outbreak of murders and other violence in Andrew County in my 1863 book, and some of the causes of it. I looked back through my notes for what happened there during the summer of 1863, but did not find a specific mention of Stephen Hill. Several active newspapers at that time kept rather good accounts of the men who were killed, so I would like to assume that your Stephen Hill was not among the dead.
Many, many Andrew Countians left the area because of all the killing, and moved to St. Joseph, or Nebraska Territory, if they were of southern sympathy. Families of northern sympathy would have been prone to move to Kansas. Of course, some families of either sympathy moved in with relatives, or to other parts of Missouri where they could start over. I strongly recommend that you look in the 1870 census reports for MO, KS, NE, IA, or other parts of MO to see if Stephen and Anna Hill show up in one of those places.
I am sorry I could not be more specific. I hope this helps you in your search.