Just a few points:
Many parks don't allow entry or set up too late, it disturbs everyone else. Most camp offices close by 9 pm. A diesel RV can be especially noisy rolling in late, not making friends among those already settled!
To do all 400 miles in one day is ambitious. Not impossible, but we have discovered we have dialed back our daily mileage to enjoy ourselves more. This from a person that in an auto thought nothing of 650-750 mile days for the past 40 years! Your distance would be best split into two days in my opinion.
In addition, I'm sure you know picking up a rental RV is not like picking up a car rental. You'll need time to have systems and equipment explained, stowing your personal gear, etc. You might get away from Atlanta later than you think.