Capt. Edmund Greenleaf, Sr. - This Edmund Greenleaf was not the same one who married Sarah Moore or Sarah Jurdain

Meaning the parents are disputed (work from child up).

The Edmund Greenleaf who came to America was not the son of John Greenleaf & Margaret Greenleaf according to Wikitree citing:

Greenleaf" New England Historical and Genealogical Register 69:358/9.

"Edmund Greenleaf, son of John and Margaret, was baptized at St. Mary la Tour in 1574/5 and he has been claimed as the emigrant. But, this man was born too early to be the emigrant, who may well have been a son of the Edmund Greenleaf mentioned in the record of the suit given above for the parents of the latter's wife Elizabeth were certainly married some time before 1576."[3]