There is a group called "
Adventure Cycling" that has created long touring routes to follow. Their "Atlantic Coast" route will get you from NC to CT. Their site says they have also created national bicycle maps, so maybe they have something to get you from Greensboro to this route, and from the route to Hartford.
Other than that, a lot of planning, maybe PM'ing folks on bikeforums for advice (especially those on the Long Distance board. I know quite a bit about the area between Greensboro and Richmond. PM me if you'd like guidance on that area...
And good luck!