I'm not sure that Elizabeth Wilford was the mother of your William South.Major South's 1st wife was an Elizabeth and his eldest son was born in NJ in 1794.The records I've seen on Elizabeth Wilford's family show them never to have been near NJ.
Major South and family went from NJ (Middlesex Co ?)to Greene Co, PA.He was there as of 1798 at the estate sale of his brother-in-law, Jonathan 'Bearmore' Baremore.Also there were brothers Benjamin and Elijah.
Major South was caught in the 1810 census in Greene Co, PA and also the 1810 census of Wayne Co, OH.Census was usally taken in the early summer - so it gives a good idea when they got to Wayne Co, OH.
The children I have for your William are:suppose Catherine (the eldest,)John W, Sophronia, Rhoda, Margaret Ida,Anderson Arthur, James Nelson and Hnery W. South.