Oregon Inlet isn’t navigable by sailboats. Not only is it shallow with strong currents, but the fixed bridge is too low. They built a 90 ft section but then it shoaled in and the USACE didn’t keep up with dredging it due to the constant shifting. The spans that have passable depths are 13 feet overhead clearance. I have not read all the details of this story but it doesn’t add up.
Well, I had thought of going south for the winter in a few years - lessons learned for my trip. Especially since I can't take the intercoastal with a 67' mast.
You will need to pick your time of transit carefully. Wait for a stable/settled forecast with mild S or SW wind and motor sail against the wind and currents. Don’t give into temptation and make a risky decision due to a schedule including crew‘s limited vacation schedule etc. You should plan on making 2-3 knots less than your typical motoring speed, but you might catch some eddies and counter currents.
Edit: Don‘t go when the wind forecast has a N component. Use the gust forecast, not the average wind speed forecast. PredictWind has a gust forecast I like to use. The Windy app also has one, and allows a view where you can see how well the different weather prediction models correlate. If they are closely aligned you have a lower risk forecast. If you see a lot of deviation you know the weather is unstable and the reliability of the forecasts is lower. (IMHO the ECMWF and GFS models are generally more reliable than others. I look for those to agree.)
Second edit: You can cross the Gulf Stream after leaving Norfolk and go far offshore, or you can stay near shore and try to stay out of the main flow of The Stream but around Diamond Shoals. Some people cut between the shoals, but that doesn’t give you much margin for error if you have a steering, engine or rig failure.
Third edit: You also could go in an E or W wind so long as there isn’t a N component. W would be smaller seas due to shorter fetch, and good sailing. However, a strong W wind would make it more difficult to turn west into Beaufort and it would be more conducive to continue to Masonboro (Carolina Beach is a great stop to wait for weather to round Cape Fear), or Winyah Bay Inlet (Georgetown) or Charleston, or further if conditions are good. Keep in mind a W wind usually clocks around to the N. An E wind would also give you a nice sail but with bigger waves due to longer fetch. An E wind usually clocks around to the SE and can often bring rain and build to stronger winds. It would be conducive to rounding Hatteras then ducking into Beaufort (one of my favorite stops) and rest the crew for the next hop south.