The only Benjamin Hinkley that I found listed in a book of Huron County Cemetery Inscriptions, who was the right approximate age, was buried in Hinkley Cemetery in Fairfield Township. However, he lived a long life, so if you are sure that your man died pre 1850, he is obviously not your man. His wife's name was Maria, and the name Polly is usually a nickname for Mary. Or maybe Maria?
Benjamin H. Hinkley died March 1, 1894, age 83 yrs.
Maria, His Wife died Jan. 20, 1896, age 85 yrs.
Two of their children are buried with them.
Mary, died Aug. 29,1838, age 5 yrs. Joshua, died Oct. 3,1844, age 2 yrs.
They apparently had at least two children who survived to adulthood, a daughter named Hannah, and a son named William. A second Benjamin Hinkley is buried in Greenlawn Cemetery, in the city of Greenwich. Interestingly, he is the only person with the Hinkley surname buried in that cemetery, but the dates are wrong. Born 1867 died 1908. There was no listing for a Benjamin with the surname spelling of Hinckley.
Sorry I couldn't find the person that you are looking for. Regards -- Richard