I've been thinking about your questions and this is as far as I've got.
First the family of Vans of Barnbarroch (in Wigtownshire, SW Scotland) is a cadet branch of Vaus of Dirleton (near Edinburgh). (The only credible information I know of about the history of the Vaus or de Vaux family at the time of the Norman conquest of 1066 is from the book "The Anglo-Norman Era in Scottish History" by G.W.S. Barrow which suggests that the family was of no very great distinction at this time). There is no doubt that they came to England with William the Conqueror. De Vaux (latin de Vallibus) became Vaus, Vans and (in Ireland) Vance.
Robert Vans Agnew (b 24 April 1755): his correct surname was AGNEW, his father having assumed the name of AGNEW at his marriage in 1747 (Robert may have been christened Vans, I do not know; he certainly wrote his name Robert Vans Agnew). Robert gave all his children the second christian name 'Vans' (ref the family bible in which he recorded this action and which is in my possession). I believe that his children did the same but that all future generations called themselves by the surname VANS AGNEW until my father, Patrick Alexander Vans of Barnbarroch returned to the name VANS in 1965.
That means that anyone called Vans Agnew is a descendant of Robert's father; anyone from an earlier branch of the family is called plain Vans.
There is only one known candidate to be your John but he has no name! He is the son of Patrick Agnew, 2nd son of John Vans who married Margaret Agnew, brother of Robert Vans Agnew (b 24 April 1755). Patrick was born 1757, married Grace Hathorne and had a son of whom I know nothing.
You can find Patrick's marriage at Scots Origins (http://www.scotsorigins.com/) and I presume that you found your John's marriage there (it is there anyway, though his name is there spelt Vance).
The Agnews also claim to have come to England with William the C, but their claim seems to be less definite.
The best place, apart from my website to find a brief genealogical history of the Vanses is either: Burke’s Landed Gentry or better still Burke’s Landed Gentry of Great Britain, (Peter Beauclerk Dewar, Burke’s Peerage and Gentry LLC, Wilmington, USA, The Kingdom in Scotland, 2001) which also has the Agnews. The Agnews are also in Burke's Peerage (Agnew of Lochnaw).
I hope that answers all your questions - if not, ask again! If you find anything out please let me know.