By the later nineteenth century, many US state and county death certificates named the parents of the deceased. I do not know when and if Ohio began to record this information but it would be worth checking if you have not already done so. As the information on parents' names was provided by whoever registered the death, sometimes there are blanks or errors in these fields and so they must be treated with a degree of caution - but they can be very useful indeed.

Good luck with your research!