Well, this little mystery has gotten my curiosity aroused. After doing a bit of research, I found this image of an American Smoke Tree......which is native to Kentucky. It's a smallish tree reaching 30'.
Kid bow, can you find out a bit more for us about this tree. More info would be a big help.
The environment this tree appears to be growing in looks like an upland woodland. Sycamore would typically be growing in a moist environment, often along creeks, rivers and areas with very moist ground.
This Smoke Tree looks very close and I found images of a northern pecan which had a very similar bark. The northern pecan can vary a great deal in appearance, so that's a possibility.
Pearly, I have never identified hop hornbeam growing in NW North Carolina, but images I've seen of the bark looks like the platelets are more squarish than the bark in the image here. BUT, bark can certainly vary considerably on different age trees of the same species.
Maybe someone will give us a firm ID before long.