Sand gets pretty deep in certain parts of the OBX, especially in the really cut up areas at the entry ramps into the various ORV areas. My cousin has a house that's 8 miles down the beach from the end of the paved road. That beach is no joke, you see tons of trucks, SUVs, etc. mired in deep ruts. I don't care how meaty your tires are, you'd be foolish to not drop your pressure to at least 10-15 PSI.
You also have to understand the difference in the environment. You guys go to Moab, where you air down/up once a day because you're in a large contiguous park. The OBX islands are sometimes only half a mile wide, so you can run the trail/beach in an hour or two. The offroad areas can be as much as 50 miles apart on blacktop roads, so you need to air up between areas or you'll eat up your tires. All this means that I may air down/up as many as 3-4 times per day. Saving a few minutes per tire X 4 tires X 3 times per day = a lot of time saved.
So it sounds like a regular air tank won't meet those needs. Are there any N or CO2 tanks that don't have to be stored sitting up?