In addition to the other suggestions, here is another sort of involved one. You could try checking for Black Civil War enlistees formerly enslaved to your family. Sounds like a long shot, but I think around 20,000 Black men enlisted out of Kentucky-- second to only one other state.
Enslavers in loyal Union slavery states like Kentucky had some hope of getting "compensation" money from the U.S. government when men who had formerly been enslaved to them enlisted in the U.S. Army, so they would sign their names to the soldier's enlistment after the fact so that they could apply for the government compensation later on. If you go to Ancestry.com, check the "U.S., Descriptive Lists of Colored Volunteer Army Soldiers, 1864" for enlistees who bear the last names of your ancestors, definitely including the women's maiden names (people were very very often "inherited" through dowries and what-all), and have a look at the scanned page and see if an ancestor's name is listed as the enslaver. Or if that doesn't work and you have the time, have a look through those records for all of the men who enlisted who were born in the county where your ancestors were enslaving people. This Descriptive List does not include former slaves who escaped and enlisted out of other states like Ohio, for example-- just people who enlisted after the date that Kentucky was given "Credit" against the draft for Black enlistments inside of Kentucky, so hence the 1864 and some of its other limitations. But if you find a connected soldier, order copies of his pension application documents from the National Archives, because these may give lots of information (sometimes hundreds of pages) about the soldier's immediate family and descendants, as part of the cumbersome process of proving identity in absence of birth records.
Best of luck in an honorable undertaking.