Hey, Matt, I live in Richmond, Va. not too many Virginians or Tarheels on this forum. I'm new to the world of TTs and have limited experience with what you are asking, but I will share what I do know.
Coming down the Eastern Shore on 13 will dump you out in Norfolk (as you undoubtedly know) into urban sprawl that rivals most anything you've experienced up North. Norfolk-Portsmouth-Va. Beach-Chesapeake is all one big city nowadays. My experience is that urban stores aren't as open to travellers overnighting as are their more rural stores.
WalMart
Walmart.com - Store Finder Results
Home Depot
Store Finder
I would make a few phone calls to some likely stores on your route to confirm if they do allow overnighting. I'll be surprised if they do.
IMHO, your best bet is to get through this area before you have to stop, or stop in Northampton Cty., Va., on the bridge's northern end. I taught school in that county and it is still rural farm country. You'd have better luck finding a business along 13 who'd let you overnight. There is a WalMart in Onley, Va. That's in Accomack Cty., close to the Md. state line.
I hope someone with more knowledge of the area hops on board.
Good luck,
Teach
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Wright Ellis and Penny Sedgley
'10 Tundra 4X4
SOB -'14 Rockwood 2604WS (
Rocky)
"Life is a cruel teacher. She gives the test first; the lesson then follows."