I know you've probably already looked at it, and that it isn't what you need. But just in case...
Rebecca Williams Harris's two-volume monograph, Daniel Williams and His Kin (Daniel, 1751-1831, being the eldest son of Joseph Williams and Mary Hicks) is digitized and available on FamilySearch: https://www.familysearch.org/search/catalog/365226?availability=Family%20History%20Library.
The books are dedicated, in part, to Thomas Hugh Williams. Some of first section of Volume I addresses an earlier immigrant, i.e., it begins with a John Williams who arrived in Isle of Wight in 1638. Also in Volume I are sections for Thomas Williams of Fayette County, Tennessee, on page 89; Thomas Hicks Williams of Fayette County, Tennessee on page 120; Thomas Hugh Williams on page 131; Thomas Arnold Williams on page 140...well, you get the idea. Lotta Thomases. Neither manuscript shows a publication date, so I'm betting that what you're looking for is likely newer, revised data. Or focused on these Williamses, but on a different line.
But just thought I'd mention it. 'Cause, you know; can't hurt to try.