Your information is incorrect re: John Barnard's wife's maiden name.
He indeed married Jane Bradley.Proof of this:
'Abstracts of Marriage Bonds of South Carolina 1743-1744' Page 96......states Marriage Bond of John Barnard and Jane Bradley, spinster'.They were first cousins.
Further proof also note the following from the William Bradley Papers:
Ref: William Bradley Papers
"William Bradley was sent to Georgia by the Trustees to teach agriculture. Embarked 20 Oct. 1735, arriving in Feb.1736.He had a grant of 500 acres 17 Nov 1735.The Trustees were calling him to account for his malversation. The Trust servants were taken from him in 1739. He was living as Inmate in Savannah on lot 37.A Rioter in open Court 20 Oct. 1735.and convicted of stealing a calf and hog 2 Nov 1737 which he confest. He too possession of his 500 acres 26 April 1739.In 1740 he left for SC "to avoid settling his account".Sometime later he returned to England.His daughter, Jane, married Capt. John Barnard of the Georgia Rangers, her first cousin; and her daughter, Martha, married Isaac Young.
This collection contains: sales account book, Nov. 1, 1753 - Feb. 4, 1755; a letter from Thomas Burrington to Isaac Young, 1759, reporting on affairs of William Bradley, Sr. in GA; one of Jane Barnard to William Bradley, Jr., n.d., mentioning Death of her brother; and another letter of Martha Young to Elizabeth Bradley, 1775, concerning her father's affairs.Also in this collection are papers of Caleb Davis, which relate to his complaint; his petition, and remonstrance regarding his treatment at the hands of civil and military authorities of Georgia.
All papers are photocopies of originals owned by a Bradley descendant in London."