Is Charlotte a must along the route? If not, you could reroute via Asheville. It does not add extra distance and is about two third of the way to Griffin. There is a nice hostel in Asheville with good ratings. (If noise bothers you take a pair of ear plugs.) For $28 you can get a dorm bed with locker assigned. (Take a pad lock.) This would get you to Griffin soon after lunch on the second day, and hopefully well before rush hour..

Yes, staying awake while someone else is doing the work is very different from being on your own, and everything is up to you. I would not worry about being mugged. On the whole the majority of folk out on the road are wonderful. I take it you have a roadside assistance plan in case of a breakdown, etc. If not, I highly recommend as a female travelling alone you get one such as AAA. You won't want to be sitting on the side of the highway with a flat tire, and you certainly would not want to stop any other vehicle. It is a small price to pay for peace of mind.

If you are carrying good maps, you will know when junctions come up, and see which lane to take. (Maps are free to members at AAA.) Do not attempt this trip with a gps alone. You should know well before the gps tells you, where to be on the road.

Lifey