I guess steep is personal in perspective really. One person may say its no big deal while another will say no way, don't do it. What is your comfort zone? You will be in the mountains once you hit northern GA. You can't avoid what you might consider steep, while someone else says its interstate normal grades. I know LA is pretty flat.
I agree though with 59 to Chattanooga, 75 to Knoxville, 40 to exit 407. I say to just go thru Knoxville and don't do 640 around it. Time of day is important though as you don't want to hit it at rush hour. Mid day is best like noon to 3pm. Plan to arrive on a midweek day, not the weekend. I have seen 66/441 bumper to bumper from I-40 all the way to G'burg.
Lots of campground choices in the area so do some searches and see which ones may be acceptable to your needs. Look at the Cosby area too. Its directly East of G'burg on rt.321.