Lol! found this a little late, but yes, you are SOL for climbs for several hours around. I spent A LOT of time near there, Topsail Island, Wilmington, etc. Near Fort Bragg has some dinky small rolling hills. Goldsboro starts to get a tad larger, and Pittsboro, Siler City, Asheboro is the closest what I would call rolling hills. Maybe up around Raleigh too. All I can say is locally, you need to do like I did living in coastal Delaware. I found one of those new, tall, large, less-used bridges going over the inlet waterways. Ride like a banshee up AND down, turn around, repeat!
Seriously- its all you have locally available. I cant remember, but I think coming out the Camp Lejeune south gate, the bridge to north topsail island may meet the criteria. Cant remember if there was a break-down lane or not. If not, be very aware while riding. Lots of bubba drivers. They dont drive friendly with bikes.
Another technique that will help is riding on windy days. I would ride with the wind in the beginning, and then ride against the wind on the way back- do it faster for more slope simulation. I know you have some steady wind available at the coast
Also, your speed isnt relative to climbing. Resistance and gear ratio being moderated with wind resistance helps your simulation.
Yet another technique is similar to being a grunt and sneaking rocks and packing into your ruck for road marches (even though you are supposed to have a standard pack out- only for the insane after 25 miles lol.) Go and buy, or find used, one of those kiddie trailers that hook to the bike. If you can scrounge rocks (another not-so-common commodity there, I know), throw them in the back, or find a biking buddy with kids that want to ride with you, and pack the kids in the back. Now, with even less wind resistance, and more weight to haul, you should be simulating grade even more!
I agree that western NC is the best east coast riding, do it whenever possible. I know that a fun day once a month isnt as beneficial as making due with what you have to deal with on a daily basis. If you do these techniques, you wont be as handicapped as I was going to visit my brother in Asheville and getting SMOKED by mountain riders. After I came up with these coastal ideas, I was on par with them climbing real hills later on. Oh yeah, if anyone wants real butt-kicker, leave Tunnel rd. (hwy 70) in Asheville, NC going up the blue ridge parkway. Ride north about 37? miles and go up Mount Mitchell. Unreal.
Let me know if any of this is useful!