Been a long time since I lived in North Carolina - moved west in 1990 - did a good deal of touring then along the cost and up to DC - some north-south - more east-west. But even then the traffic along the coast was getting nasty. With all the coastal development since then it's probably four times worse. To be perfectly honest, the AC route seems pretty sucky to me. Why bike thru Richmond, DC, and Baltimore unless you really have to??
I think you would be MUCH happier biking the Eastern Shore and crossing over to Jersey on the Cape May Ferry. then you can bike thru Wharton forest and up to Atlantic Highlands and come into Manhattan via the Express Ferry.
One of the basic problems abou biking the East Coast is that you have many river and estuary crossings to deal with. In the olden days before 4-mile-long bridges, ferries would shuttle cars and what few cyclists there were. Now all that traffic rushing to the beach is squeezed across a mega-bridge. Bridge crossings are always the issue - even inland - since the rivers are fairly wide.
You can check state DOT sites for traffic volume.
For example - South Carolina's is here -
I checked Horry County against the AC route - 7000 to 11,000 AADT
Average Annual Daily Traffic -
Rough Rule of Thumb -
Under 500 - Nirvana
500-1000 - Nice
1000-2500 - Okay, but you start to want a shoulder
2500-5000 - Busy and really need a shoulder
Anything over 5000 without a shoulder really sucks
(Even with a shoulder it's a constant stream of cars.)
WABA has information on Washington area routes.
The general consensus is that there is NO good way to get from Richmond to DC.
I know the NC coast best.
The stretch north of Cape Hatteras to Nags Head is really busy.
Ocracoke Island is wondermous.
I recommend taking the Cedar Island Ferry to Ocracoke - base there.
If you want - ride up to the Hatteras lighthouse and back on an off day.
Then continue north on the Swan Quarter Ferry.
(I think the ferries are $3 per cyclist - the best ferry bargain in North America.)
From Swan Quarter, take the NC 94 across Lake Mattamuskeet to Columbia -
Then back roads to Pettigrew State Park - on a huge lake.
Somerset Plantation - in the middle of the vast swamp - is right next to the park.
Then back roads to Edenton - a superb colonial town.
You can find NC County maps on line
NC 94 has an AADT of 530 north of Lake Mattamuskeet - - truly sweet.
(NC 12 has 5300 at Oregon Inlet - and probably over 10,000 near Nag's Head.)
I'd cut east in Virginia - taking care to cross the tidewater rivers in the best locations possible
And cross over to the Eastern Shore via Tangier Island to Crisfield, Maryland -
Then take great backroads to Cape Henlopen in Delaware.
It's a challenge, but you can find better routes than the AC.
Best - J