If we are in a hurry we just go to Montgomery and stay on I65 to I20 and then take exit 188 to the Leon Smith Parkway and on over to HWY 281 which approaches the park from the Northeast. HWY 281 is very steep when close to the park but not a big deal.
Usually we are not in a hurry and at Montgomery we take I85 east and turn north on Hwy 49. We then turn northwest on HWY 77 toward Ashland and then take Clay County 31 to Highland. Then take the small county roads to HWY 281 which approaches the park from the southwest. Sometimes it seems like it takes forever on this route because it is a slow drive through small towns (with stop signs) but it is a pretty area and you get the bonus of stopping in at the Horseshoe Bend National Military Park if you want to. It is a nice 1 to 2 hour stop if you like that sort of thing. We do this with an F350 and a 28ft fifth wheel and we have no problems.
