Red River Gorge Scenic Byway (Kentucky)

I assume you mean the NADA tunnel-Sky Bridge loop. There are several park and ride (carpool) lots at Mountain Parkway exchanges in the area. It would probably be easier to park in one of these lots and take the toad. I'm not sure of the height of the NADA tunnel. It would probably work, but the roads are so narrow passing another car requires concentration. There are tight switchbacks and at least one one lane bridge.