You might do it in your timeframe but what would be wrong if you arrived at BCV by 3pm Saturday? If you get there earlier, good deal.
BTW, you did pick up on the fact that you continue south on I-77 to I-26, didn't you? Don't take the I-20 to I-95 cut off.
Also, I would drop the speed down about 5mph at certain places in NC and SC. From time to time, I have seen cars pulled over between Charlotte and Columbia on that great stretch of I-77 where you could do 85 easily. Also, from time to time, especially on the section of I-95 in SC below Walterboro and above Hardeeville SC, I have seen state police working both sides of the road where you wouldn't think they would be. Of course, you may not have that problem.
Also, just a personal recommendation is to switch drivers every 2 to 3 hours during that period between midnight and 6 am. A good break is at the last Harrisburg exit(Exit 52) on I-81 near the PA turnpike. A good break is at Harrisonburg VA on I-81 near James Madison U. A good state welcome center (only for potty break) is the one coming into NC just below Fancy Gap VA on I-77. If you need to stop before that, the first exit just south of the I-81 and I-77 intersection at Fort Chiswell is a good one to take a break. It is just a mile below that intersection, the gas prices aren't bad, and there is a good truck stop there. Another good break is the first exit just west of the I-77 and I-26 intersection on I-26. It is easy on and off and the gas prices are good as well as a very active Pilot/Wendy's there.
Also, in GA just north of the Florida border, exits 6,3,and 1 are good (near Kingsland GA) to stop and get GA gas prices.
Have a great trip and be safe.