Yep, the cut off is often very sharp on the western side as well. Areas back towards Charlotte & the SW Piedmont of NC in your neck of the woods rarely do all that well compared to others w/ big coastal storms. Dec 2010 imo is the single example that best sums up how the snow distribution tends to shape out w/ Miller type A cases.
Bullseye over US HWY 1 to I-95 corridor (RDU & points just east), with another, arguably more prominent area of higher snowfall over the NW Piedmont into the mountains.
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For the SW Piedmont of NC & upstate SC (Charlotte + Greenville-Spartanburg area roughly) to get "bullseyed", you usually need to see an overrunning event (e.g. Jan 1988), a CAD that's cold/deep enough s.t. you can snow a lot into it via warm advection before changing to IP/ZR (e.g. Feb 2014), or an upper level low. Some historic events like Feb 1969 & Feb 2004 have more than 1 of these present.