Back in the late 70s I drove from Tucson AZ to Patchogue LI NY in a car, I was the only driver. I planned on doing it in a few days but did it in 2. First day Tucson to Amarillo TX with an overnight motel stop. The second day I got bored and just kept on driving till I got home. I flew between NY and CA many times but this time I wanted to see everything in between. I soon realized that if I wanted to see and enjoy all the good stuff in between I would need a week or more. Driving a car does not require as much concentration as an RV. It would be cheaper and more cost efficient to fly and rent a vehicle. I do push myself if necessary but in my case I have discovered that if I drive a long distance almost non stop I will probably need 2 days to recover and rest up, or I drive3 days I arrive rested and ready to go. Maybe you will be able to rest while some else is driving.
To answer your question there is little doubt that the trip can be made in the allotted time I just have this gut feeling that what ever time you save driving non stop will be lost when you need to spend a day or two to rest and recover.
The last time I drove non stop between NY and SC was over 7 years ago My physical condition has gotten worst as has my medicals.
Enjoy your trip and do not take any risks that can put you in a hospital. If you mess up there aren't any reset buttons and do-overs
By the way I always try to drive at night to avoid traffic, but if I am driving something big like a truck or RV I prefer daytime driving