My research methods are mostly grunt work fueled by cognative radar.I went through all the legal records of West Jersey I could find on line and found where the Quakers, in particultar, immigrated from.Then, what was interesting, was that the VA. William, had John Gregory from Wantage, Berkshire, England, who married Elizabeth Armstrong (which was noticed by another persons post)as a neighbor.This may or may not tie him to our William, but it is interesting.
I then reseached all the Berkshire locations and did a distance mapping of these areas and found they are very close together.Whitechurch is just miles from Wantage and here we find Simon Akers.I may be wrong, but I don't remember Simon being a common name in other Akers lines.
I don't know where the information that William the Quaker was Jr. came from, but the Wantage William was listed as the son of William who married Joane Hyne in parish records.
So. We have William Jr. who is a Quaker in West Jersey in the midst of a bunch of West Jersey Quakers who came from Wantage and surrounding areas.Our William was not only in good standing with these men but a trusted leader.This implies a strong multi-year relationship, perhaps from the "old country."
There are a few more layers of reasoning but that's the basic idea
The evidence is really telling my gut my that our William is that William.Mostly, I am hoping others will dig deep too and finally pull this together.