This is preposterous. I am flabergasted, that someone would not pass a property and ok it for close because of think it is unsightly, when it meets code.
As a matter of law, he has to fail the inspection for matters related to law and code, not to his personal judgment about the esthetics of the driveway. Ok, the drive way is ugly, but it meets code.
None the less, I am familiar with the "good ole boy" attitudes in NC of state and especially locall officials in your town. (I was stationed in Ft. Bragg with Special Forces for a nubmer of years, and spent a lot of time in the hills of the Natioal forest and other places).
I believe your solution should work. I would use a piece of expansion joint in the quarter inch slot.
It almost seems it would have been easier in the beginning to have gotten an easement or signed an encroachment agreement with your neighbor.
You can pour a new corner piece that falls short of the other property. That might be more esthetically beautiful. (not the whole driveway, just the corner).
You already signed the closing documents. if you already signed the closing documents, it is a moot point. So you are really just trying to get this guy off your back untiil you get the occupancy certificate and can move in.
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