See: Anderson, Robert C. The Wives of Michael Barstow and Richard Carver of Watertown, Massachusetts, and The Identity of the Wives of William Randall of Scituate and William Perry of Marshfield. The New England Historical and Genealogical Register, Volume 146 pp. 230-4 (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2001-2013.) Requires subscription: https://www.americanancestors.org/DB202/i/11691/230/235119294
Robert Anderson has postulated that Susan (sic Barstow) that married William Perry, is the daughter of Richard Carver and his wife Margaret Skurrie as follows:
Richard and Margaret (Skurrie) Carver had twin daughters, Elizabeth and Susan, baptized at Filby, Norfolk on October 15, 1618. Margaret was buried shortly after the birth of these twins on November 16, 1618. Richards' second wife Elizabeth died in 1622.
Richard married 3rd, Grace Walker in 1623.
Richard Carver, wife Grace and their twin daughters Elizabeth and Susan Carver sailed from Yarmouth, Norfolk to New England in 1637.
Richard's will written in 1638, was proved on September 9, 1641 leaving his estate to Grace, Elizabeth and Susan.
His widow Grace, married Michael Barstow, as his third wife.
Michael Barstow had no children by his three wives, so the Susan Perry, wife of William in his will would be his stepdaughter Susan Carver.
Change he LNAB to Carver based on the above - or change to Unknown as this has not been proven?
See also G2G: https://www.wikitree.com/g2g/537400/disconnect-william-barstow-alleged-children-matthew-barstow