Least challenging would be to backtrack to Bakersfield then 58 (past Orange Grove) to Barstow and hit I 40. Start real early from Bakersfield and try to get past Needles before the afternoon heat. Things should cool off From Kingman To Tecumcari where you have descended to flatter landscape. If mobile stay on 40 to Memphis and I 55 toward Mobile. If Bowling Green go to Nashville and turn toward Bowling Green. You know after Amarillo it will be HOT and HUMID.
I have never driven Tioga pass, but if you are comfortable driving it you could take the pass down to 395, then North to HWY 50 in Carson City. Hwy 50 to Utah(the lonliest Highway), then I 70 into Denver (Grand Junction, a side trip to Moab Utah, Vail Colorado) and across to St Louis or turn right in Denver head to Colorado Springs, Pueblo, and blue Highways to Wichita Ks. Then pick and choose to Mobile or Bowling Green from either St Louis or Wichita. These routes are more challenging than I 40 and the drive across Nevada could be stifling. With the exception of Tioga Pass I have driven these routes. Each offers its own uniqueness and different scenery.
2008 Jeep Sahara '4Dr"