Hello.
After looking into birth, baptism, marriage, and death records, I've come to the conclusion that these 2 John's are one in the same--not so much like identity theft, but rather split identity.
Firstly, according to the LITTLE CHUTES HISTORICAL SOCIETY.org, Alice Turberville did indeed exist, was born in 1577 in Woolbridge, with the name of her father being Matthew--which makes sense, her naming the firstborn after her father. But here's the kicker: Alice's first 2 children were born in Exeter-Devon, near Woolbridge. However, my great grandfather x9 her 3rd child, Christopher, was not born in Northern England but rather back down 300 miles south in Yorkshire--in 1608, where nearly ALL of John and Jane Grant's children were born (2 years after Jane's death).
I believe he had 2 separate families, with overlapping births from both wives. Since divorce and remarriage (or bigamy, for that matter) became a felonies in 1604, I suspect he felt the need to create a separate John Grant on paper, and since he was the Vicar of Caverley Parish, this would be doable.
Through various genealogies and church records, I have located 2 John Grants, one born in 1573 and one in 1568, both with parents George and Julian Clargennet. I even found one church document that claims John Grant's wedding date to Jane Watson and his day-of-death as BOTH July 22, 1593--before he conceived 9 children with her.
It makes sense, why all 4 of John and Alice Turberville Grant's children migrated to the New Colonies, 3 of them settling together in the Watertown, Massachusetts area. There must've been much bitterness. My great grandfather x9, Christopher, appears to be the only one who ever spoke of his parents. Matthew Grant (President Ulysses S. Grant's migratory ancestor) never disclosed the name of his parents. He did, however, with "some sadness," report that "On 29 May 1640 mother...Grant had died" at Windsor, England. (In fact, Alice Turberville died on May 31st.)