As far as I know, NC has no antique plates, however:
You don't need an inspection on cars 35 years old or older.
You can run a plate from the year of your car provided you keep the "real" registered plate under the front seat for easy access if pulled over by law enforcement. NO, the number on the vintage plate is NEVER recorded by the DMV. You could literally run a different plate every day of the week.
To avoid paying propert taxes (YES, cars are taxable property here), you can run a transporter tag as long as you're going to/ coming from a car-related event. I suppose you could mount the vintage tag and keep the transporter under the seat. ("Tag" = "Plate" LOL)