Nylon I do this route frequently a year from NY area but in a car mostly. I can tell you that there are great areas running the DE, MD, VA route from 1 to 113 to 13 to 17 but there are lights and you might run into a few gas stops with height restrictions along the route. Trucks use this route to the chicken plants so it is accessible just stopping can slow you down with a load.
The BBT (23miles long) has one gas stop north that puts it about 40 miles between fill ups then you get to go through Norfolk VA and there are a few more lights and drawbridges, traffic that you will encounter especially if a drawbridge is up or scheduled. Been there done that
. not fun.
From the Dismal Swamp to New Bern is a good 3hr run with few lights(new bypasses) and not too many gas pumps to hit either. Once you hit New Bern more lights and so on. 11-12hrs to New Bern towing and 4hrs to Myrtle with no traffic. There is a KOA before the Nuese River bridge in NB if you need a pit stop.
Sooo...if I were towing I would leave 84 Newburg area at 10PM go 287 to NJ turnpike to 95 and get through DC area by 5AM then take the 501 right into MB from there. If you can get past Richmond, VA before 6AM you should be good.
Coming back however you will need to consider the same rules with getting past Richmond and DC area. The 64 feed from Williamsburg and VA beach can be a disaster during weekends and other parts of the week so try to avoid leaving at peak AM times if at all possible. I've seen it backed up for miles and miles.
I've heard bad things about the 81 route but only one source so can't comment on that routing. I've done it every time of the day and night seems to be best for 95. Daylight has always been a disaster. If you leave south at 5PM though I have had good luck in doing that where you hit DC 10PM or later.