I think Jas is not so much a nickname for James, as a written abbreviation. In old English and American documents you can often find abbreviations for the most common men's names:
John = Jn. or Jno.
James = Jas.
George = Geo.
William = Wm.
Thomas = Tho. or Thos.
Henry = Hy.
Robert = Robt.
I'm sure there are others.