William Wadsworth, II - Questions of Places

Here on Geni, William Wadsworth, II shows birth in Long Buckby, Northamptonshire and his first wife, Sarah Wadsworth , shows birth in Braintree.
William’s second wife, Elizabeth Wadsworth , shows birth in Long Buckby, Northamptonshire. Thus it seems that the Wadsworth and Stone family comeovers probably knew each other prior to emigration—if William was indeed born in Long Buckby.
Wikitree believes 2nd wife Elizabeth and her siblings were all baptized at All Saints and St Church John, Hertford, Hertfordshire: https://www.wikitree.com/wiki/Stone-189 .

A question arises as to whether birthplaces from 1st-marriage children, which show “Braintree”, are well-supported in secondary sources.
Long Buckby and Braintree are 94 mi or 151 km apart. I’m not sure if there’s an extant source connecting the dots or if there's a well-reasoned historical rationale vouching for William's removing from Long Buckby to Braintree at some circa year. Anderson’s Great Migration offers neither.
Below is what Anderson says about the children of William and Sarah, which does not suggest birth/bapt. locations:

1. daughter Sarah Wilcox shows birth in Braintree, Essex. – Great Migration: “SARAH, b. say 1626; m. Hartford 17 September 1646 John Wilcox [HaBOP 525; HaVR 607].”
2. son William Wadsworth, III shows birth in Braintree, Essex. – Great Migration: “WILLIAM, b. say 1630 (adult 1653 [RPCC 117]); m. ____, who d. 1659 [Grant 82]; not named in father's will, 16 May 1675.”
3. son John Wadsworth, of Farmington shows birth in Braintree, Essex. – Great Migration: “JOHN, b. say 1632; m. say 1658 Sarah Stanley (eldest child thirty-one years old in 1689 [Manwaring 1:514]), daughter of Thomas and Bennet (Tritton) Stanley [TAG 32:199, citing HamPR 1:55].”
4. daughter Lydia Wadsworth shows birth in 1634. – Great Migration: “LYDIA, b. about 1634 ("Wadsworth Lidia above 24 or 25 y.," 7 July 1658 [WM] 117]; "Wadsworth (his eldest daughter) Lidia about 20 y. [sic]," 3 May 1660 [WMJ 201]; about twenty-six years in September 1660 [WM] 2171); not named in father's will, 16 May 1675.
5. daughter Mary Stoughton shows birth simply in England. The Great Migration suggests otherwise: “MARY, b. say 1635; m. Windsor 30 November 1655 Thomas Stoughton [CTVR 42; Grant 65], son of THOMAS STOUGHTON.”
   1. Curiously, Packrat-pro includes Mary on its passenger immigrant list with her family, which may well be an error: https://packrat-pro.com/ships/lyon4.htm .
   2. If Mary was born after her parents migrated, then she was likely born either in Cambridge or Watertown per Anderson’s timeline rationale: “CHURCH MEMBERSHIP: Admission to a Massachusetts Bay church (probably Watertown) prior to 6 November 1632 implied by freemanship.” Her father removed the family to what would be Hartford, CT in 1636: “About 100 Puritans, led by the Rev. Thomas Hooker, created a settlement on the banks of the Connecticut River in June 1636.” – https://www.hartfordhistory.net/founding_of_hartford.html