Simply, no if you are going to the park from town (from the west heading east). That area is just that way. We go to Mountain Lakes Resort down there and we enjoy the area. I come in from the east and head west to the resort. There is no terrible hill to deal with this way but it is 2 lane
and can be narrow in places. That is really the only option for a road to the park. I am aware of the hill you speak of and it is fairly steep and twisty but that is really the only grade of that magnitude to deal with. You can do it.
Look at the map for 35 out of Scottsboro, it takes you over the river and then almost immediately at the end of the bridge you will pick up 67, that will run into 227 that the park is on. I pull my 37ft trailer on it so your C should be OK on it too.