Until a few weeks ago, I had no idea that Asbills had hit SC before 1799. After seeing your post, and if I can ever get home again (I've been in Guam for six months!),you can bet I'll be parked in the Charleston Co. library's geneology room, pulling data from Berkeley and Kershaw counties :).
These are the only Solomon Asbills that I know of in your time period. I don't know if the following info. will help, hinder, or confuse you, but since I've got it, I thought I would post it.I received this via email from someone with Bertie Co., NC transcribed court references.This is pasted as received.
Bertie County Court Records [abstract by transcribed by Weynette Parks Haun]
in vol II: 1. April 14 1760 - Solomon Asbell records ear Marks and brand [S A on left buttock] a deed of sale -- Solomon and Mary Asbell to William Homes - proven by John Francis Spivey[Mary is daughter of Joseph Thomas, dec [in deed]]
2. - Oct 1762 - witness of deed of sale Michael Thomas to John Hill (I'm assuming this is Solomon who witnessed the sale, AA)
in vol III: 1 a. -85 - Sept 1769- ordered that Joseph Azbell orphen of Solomon Azbell decd aged about six years be bound as an apprenctice to Malachiah Frazer to learn the trade of a Cooper. 1 b.- ordered that Solomon Asbell orphen of Solomon Asbell deceased aged about five years to sd Malachiah Frazer to learn the Trade of a Cooper.