I can't give you the exact line, but I believe you will find that the Laurel County, Ky., Sturgills are descended from the Sturgills of Grayson Co., Va. and Ashe Co., N.C. (these are adjacent). The migration was probably in the early 1800s. There is a small community that is still called Sturgills in northern Ashe Co.
(I am a distant relative also, but my Va./N.C. Sturgills went to Ohio in the mid-1800s.)