I-24 thru Chattanooga to I-75 south will shorten your trip 90 miles. Yes you will have to cross Monteagle Mountain. Coming from Nashville it about 4 miles of 5% up and 5 miles of 6% down, with about 2 miles of near flat across the top. I wouldn't go 90 out of the way, but that's me. You could come down I-75 thru Cincinnati, OH. You would then have to cross Jellico Mountain. The grades are about the same, but southbound you would climb the steep side. Mileage between I-65 and I-75 is near equal.
2018 Silverado 3500 DRW
2011 Montana Mountaineer 285RLD