This is a tough one.
I don't think there will be a lot of commute traffic next week due to spring break. That's typically how it goes. I think more people will be likely to leave DC on Saturday or Sunday, and not Monday.
I've been going to NC a lot (to that general area, OP... I'm SOOO familiar with every inch of I-95) and leaving on Thursday mornings works pretty well. I return on a Tuesday or Wednesday. Of course, you don't have that option.
Honestly, I don't see one time being clearly better than the other. If you are fine to drive at night (including sunset), then maybe Sunday. But if night driving isn't your thing, leave Monday. I can't deal with sun directly in my eyes, so I'd be opting for Monday. My husband has no issues with sun bothering him, so we'd probably leave Sunday night.
Oh, enjoy some Haley's ice cream for me. I grew up going to Holden but hadn't been back for about 30 years until a few years ago when we were at Sunset Beach and hitting up restaurants at the other beaches. When we stepped in, it was like I had teleported back to my childhood.
And if ice cream isn't your thing, then there's always the organized chaos of Provision Company.