The four region model of the US is useful for keeping statistics, but it's not very helpful in defining political and cultural geography. A better reference is Joel Garreau's work
Nine Nations of North America which goes into the details about what makes up the culture of each region and where to best draw the lines. Here's his boundary for Dixie from the Atlantic Ocean west to Louisville.
As to the DE debate, my best man lived in southern DE for twenty years, and I had many visits to the area. I agree with Garreau that southern DE and the Eastern Shore of MD fit in more with the Carolinas than they do with Long Island (where I spent much of my grad school research time).