The problem with the Virginia barrier islands is that fourteenl of them (Hog Island in particular) are owned by the Nature Conservancy and they do not allow camping. Only the ocean islands are campable as all the rest are marsh islands with no dry ground. There is a Coast Guard facility at Quinby Inlet that would be a possible camping spot. But in any case I would not leave a camp up, but would break down each day and stealth camp. The largest town out on that side of the coast is Watchapreague but I do not know if they have rental boats.You also might check Oyster and Quinby but they are much smaller. You might be able to rent a boat at Chesapeake City but that is on the inside of the Cape and quite a distance from the Virginia Islands. Depending on the type of boat you rented it might be feasible.
The southern portion of Smith Island has a beach, I know that Ship Shoal Island and Paramore Island and the north end of cobb Island have sufficient height to support a dry camp.
The Conservancy is likely to be more protective and more active in the spring during the bird migration.