Re: William Randall b. abt 1609 England

William married Elizabeth Carver daughter of Richard of Watertown MA not Elizabeth Barstow. The confusion arises because Richard's widow married Michael Barstow. See the article in NEHGR vol.146 [1992]page 230.
Elizabeth's mother was Margaret Skurrie who died in 1618 in Filby, Norfolk, England. Richard remarried and came over in 1637 with wife Grace and twin daughters Elizabeth and Susanna. He died in 1641.