FWIW, California DMV registers specially constructed vehicles the same as the NC DMV person is stating. My SAS replica is registered as a 2013 special construction, the year of build. In California, owners have the option of registering specially constructed vehicle in two ways: 1) by the year model the replica represents (1957), or 2) by year of engine manufacture (2008).
Everyone I know chooses option 1, so that smog testing is never required. Not sure how it works in NC, but I hope the above info is helpful. At least it would be worth a question to NC DMV if their process is similar. Best of luck.