Once upon a time over 20 years ago I had been diligently trying to follow all possible trails from Robert Abernathy of Virginia back to Scotland. I kept finding that most of the trails could not be documented to my satisfaction.Eventually, I tracked down the official penultimate UK source for the one trail that many here in the States claim is the correct one, only to find it is NO SUCH THING! That penultimate source very firmly squashed it, as did several other sources I've subsequently examined in great detail.
I an doubtful if you can document your William, either. For one thing, you've got his death year wrong, and probably his birth year as well. Something I would have expected if the sources you are working from are the LDS Pedigree Files. I do not trust those nor VERY few of the IGI records, either:in my experience, most have proven to be unreliable garbage!