I see this post is old, have you had any luck?
The cemetery caretaker in Wessington Springs asked me to research a request by a family member of Justin Schmit, as they are located in France. Justin was the brother of his grandfather. They have a picture of his tombstone. It is not in any Jerauld Co cemeteries that we know of, even though that is what they thought. They were also wondering about the cause of death. The next rainy day I get, I can check the courthouse records in Jerauld, and if necessary, Sanborn County too.
Being a Schmidt myself, and that my family was part of the Catholic community in Woonsocket, I am familiar with the cemetery, for the most part. You commented on the 1910 Census page that their names are spelled wrong, and they were friends of your family. I would like to find the marker myself, as sometimes they yield clues.
I would very much like to help. Genealogy is a passion of mine, and I am also a member of Findagrave.com. (I'm updating Prospect Hill Cemetery in Wessington Springs, complete with photos of markers.) That's how this task was passed on to me. Please update me on your info, and hopefully we can get the mystery solved!