John Fenimore d 1778, of Springfield twp, listed his house at Slabtown (Jacksonville) and named each of his brothers and sisters in his will.His wife was Rachel Carson who he only married in 1775 and they had one daughter Sarah.
He also left a legacy to John, the 'natural son' (illegitimate) of Rachel King, now Norcross, when he becomes of legal age.
John was the son of John Fenimore (b bef 1713-d 1777) and Sarah Brian.He was prob b abt 1737.His father was a son of William Fenimore (b in the 1670's-d 1721). His father was Richard the immigrant. (James Fenimore Cooper was descended from the immigrant Richard's other son Joseph)
I don't see an unattached or early Rachel Fenimore at all.These early generations are quite well documented since many were still Quakers.They also left wills and listed children and grandchildren.
The Rachel Fenimore closely related to James Fenimore Cooper md John Heaton 1774 and then Robert Thomas 1784.
John Fenimore (of the above will) had a brother Joseph whose daughter Lucy Fenimore md Simeon Norcross - half brother to the above John King.
These descendants of the William (d. 1721) line lived out in Springfield twp rather than in Burlington.
My guess is that John Fenimore (of the above will) was perhaps the father of your John King. He doesn't say that in the will but why else leave him a legacy?And he didn't marry until he was almost 40 years old.