Have you ever been to the Outer Banks of NC? There are several campgrounds right over the dunes from the ocean on Hatteras Island. KOA, Hatteras Sands, Ocean Waves and Frisco Woods is on Pamilico Sound.
Searsport Shores is very nice, or at least it was 4-5 years ago. Not surprised that Hampton is booked - it is very small and always crowded. We prefer Salisbury, which is only about 5-6 miles south. Very large, and you have to deal with Reserve America, but you could probably still find a spot, and the ocean is, once again, just over the dunes.
Good luck - New England is great, but so are the Outer Banks. My daughter lives there.