Working backwards from Indiana. William Hall, signing as Captain William Hall, signed a petition to Congress to support George Ash's claim to land around the lamb area. The petition was dated Feb. 5, 1802. William and John Hall were named to the militia for Hamilton County, Northwestern Territory on July 5, 1802 (the transcription says Hull, but it's clearly the Halls). Since Heathcoat Pickett, the pioneer settler of Switzerland County was also named an officer, it's clear they were already in Indiana. At the time, Hamilton County's western boundary was the Greenville Treaty line.
Although his son John married Elizabeth House in Gallatin County, Ky., in 1803, this is not a serious issue. Many people crossed the river to get married for lack of JPs and ministers and at that time, Carrollton (then called Port William) was in Gallatin County.
I seriously doubt that the Halls were in Indiana much before 1802
I have a suit that was filed in Jefferson County and it showed that William Hall was living on a certain road and gave a year--I think 1796. I can't seem to find it at the moment. That's the earliest I can place him in Kentucky reliably.
Hall swore on 15 Apr. 1835 in support of Levi House’s Revolutionary War pension application that he had known House since Hall was 13 or 14 years old, which would be in the late 1760s or early 1770s. When House enlisted, Hall lived on 10-mile creek in what is now Washington County, according to his affidavit