This book might be helpful. From google you can tell it has references to the Burt family, but as it has snippet views only, the actual book needs to be found. Maybe a local,historical society would have a copy.
History of Lower Scioto Valley, Ohio: Together with Sketches of Its Cities, Villages and Townships, Educational, Religious, Civil, Military, and Political History, Portraits of Prominent Persons, and Biographies of Representative Citizens,
Windmill Publications, 1884 - Scioto River Valley (Ohio)
I've also added some familysearch.org references to the profile. Hope this is useful to you.
I also located a newspaper article about a Rev. Benjamin Burt who ran a way with one of his parishioner's wives in 1872 in Portsmouth, Scioto Co., Ohio. I don't know if this is the same as your Benjamin. Here is the link. https://www.newspapers.com/image/56315691/?spot=3143918