Once I calculated the approximate birth date of William of SC in relation to other Hillhouses, it became clear that he was too old to be a grandson of John of Free Hall, so must be the son William. I had not looked at this closely until you brought it to my attention. As others have noted, Hillhouse & Petigru do not give adequate documentation on all their material. I am excited by this new information and the hope of getting the line clear.
Hillhouse & Petigru state that Abraham Hillhouse, son of John of Free Hall, was heir to Free Hall and ancestor of Hillhouses remaining in Derry. There are or were Hillhouses in Bristol, England, who were ship-builders there for several generations and perhaps they have direct-line male descendants. (An acquaintance in Savannah years ago had a very fine pair of ca. 1750/60 Thomas Gainesborough portraits of the James Hillhouses of Bristol.) Perhaps a search of living Hillhouses in Bristol and County Derry might turn up male descendants of those branches of the family.
You ask about my screen name. I am not descended from Jost Hite, but his son/grandson Major Isaac Hite married my cousin Eleanor "Nellie" Conway Madison, as his first wife, and by interesting coincidence, my great-great-grandfather who was married to the Madison cousin (via the Catletts) was killed in the Cedar Creek battle of 18/19 October 1864 at Belle Grove, and is presumably buried somewhere on or very near the Belle Grove property. The Hite in my address comes from a phoenetic form of my mother's family, Hightower, combined with a contracted form of Moore.