I'm a Schaeperkoetter but I'm not a descendant of the Gasconade Schaeperkoetter's. However, I do have some information that should be useful for you.
First, there was a Gasconade history book that various families in Gasconade submitted their stories to. One of those stories was about the family you're looking for. The story is a bit long so I'll post another message with other info that I've found.
Here's the text from the history book:
Friedrick "Fritz" Schaeperkoetter
Friedrick "Fritz" Schaeperkoetter at age 5 arrived in Gasconade County in 1858 with his family, having traveled from Borgholzhausen, Prussia, Germany. The family consisted of three brothers, three sisters, his mother and step-father Christopher Heinrich Juedemann. The route of travel to this area was much the same as other German immigrants. Travel by ocean to New Orleans and then inland by way of the Mississippi and Missouri Rivers. New Haven and Hermann were popular debarkation points. The first home of the new German-Americans was on the farm that is now owned by William Boettcher between Bland and Owensville. Fritz married Wilhelmine Bentlage. Their parents attended the same church and the children played together while both families were in Germany. The Schaeperkoetter-Juedemann migration preceded the Bentlage's by eight years. Fritz was confirmed in a church of the same denomination in America on the same day that his future wife was confirmed in the church both had attended as children in Germany. Married February 22, 1876, the two lived on the farm for 17 years before going into the mercantile business in 1893 in Mt. Sterling. Prior to the move, six children were born: Anna, Christ, Lotti, Louise, Minnie, and Louis, who died after nine months. Fred was born after the move in 1895, the first of seven male Schaeperkoetter's to claim they were from Mt. Sterling. Anna married William Wissmann, four children were born to this union: Arthur, Cora, Elmer, and Virgil. Christ spent his life in the retail business in Rosebud and Bland while rearing three children: Alvin, Violet and Fern. Lottie married Sam Schneider and their two children, Pearl Schwegler and William, both live in Linn. August Landwehr married Louise and farmed in Mt. Sterling. Three children were born and all still live in Gasconade County; Helen is Mrs. Chester Hesemann and Waldo and Homer are on the home place. Minnie married Louis Strunk and their two sons, Norman and Marvin, live n the Chicago area. Fred has been in Mt. Sterling all of his life, operating the business his father started, from 1920-1947 as an individual proprietorship. In 1947 the business was divided into two corporations. Fred married Sylvia Opitz and four children were born: Raymond, Ivan, Bill and Vida. Raymond married Cecilia Pollock and lives in Salem, Illinois. Vida followed Fritz's brothers, descendants to Lafayette County. She lost her first husband, Edsel Schneider, and is now married to Alvin Mehroff. Her son, Dennis Schneider, is engaged in farming and has three of Fritz's great-great-grandchildren. Ivan married Ramona Koenig of Bland and is the manager of one of two corporations that evolved from the original work of his grandfather. Their two daughters are both teachers. Mona, is married to Dr. Carroll Zahorsky, in Raytown and Marica, is married to Terry Perrella, in Linn. Bill married Eloise Miller of Hope and is the manager of Schaeperkoetter's Sales and Service. Mark Jeff, Brian and Julie were born to this marriage. Mark works in The Citizen Bank of Owensville and married the former Judy Wheeler of Raytown. They have one child, Seth. Jeff is an attorney in Owensville and is married to Jane Alfermann. They have two daughters and a son that are the only great-great grandchildren of Fritz that bear the family name. Brian and Julie attend Southwest Missouri State University. Brian is a seniorand Julie is a freshman. One hundred and twenty years after Fritz's arrival, the language, the customs, and the country way of life have changed but his descendents live on in the county that is so full of the heritage the he helped establish.