I am curious on why you would not suggest either I64 or I66 off I81 to I95 South to South Carolina.
That route was my take on a fairly direct route to Myrtle Beach.
I-66 and I-64 are both great for side trips. They are not the easiest and/or quickest for going to Myrtle Beach.
66 to DC area is good, and there are a lot of things to do, that way. I could recommend going around DC, and taking US-50 across to the Eastern Shore and down the coast , and across the Chesapeake to Norfolk via the Bridge Tunnel, and south from there.
I-64 is great, if you trip includes a visit to the Norfolk/Va Beach, area. And if it does, then I recommend taking the side trip to Kitty Hawk. And if that works for you, I recommend, from there go back to US-17, and follow it the rest of the way down to Myrtle Beach. That is a nice drive, if you're not in a hurry. I'd even recommend finding out if your rig can fit on the Ferries at Hatteras and Ocracoke, and take that route.
Those are fantastic side trips. You could spend all Spring and summer just going to Myrtle Beach that way. If you have the time, by all means, Go for it. You will not likely be disappointed. I kinda wish I could go along. And I haven't even touched on all the side trips, like the Colonial and Revolutionary war historical sites, or the American Civil war Historical side, or the amazing Fishing opportunities, and some of the finest beaches in the US.