You don't have to go into Ohio. Take I-74 toward Cincinnati, but get off at x164, State Road 1, and go south toward Lawrenceburg. Get on I-275 (x16) where IN-1 intersects US-50 just north of Lawrenceberg and go south, cross the river, and you are in KY without having gone into Ohio.
And this saves about 30 minutes off the trip.