I have been able to find rather esoteric sources that are underutilized and beneficial by scouring the source lists, per person, at "Famous Kin."
For the main person of interest, whose origins are in dispute, the below should be vetted (noting that at least one or two overlap with a presently cited sourcing on the person's profile page):
Sources listed for Thomas Carter (ca. 1650 - 22 Oct 1700) by Famous Kin
1 Carter, Jeff, Ancestors of Jimmy and Rosalynn Carter, Jefferson, North Carolina: McFarland and Company, Inc. (2012), 13, 24-32.
2 Miller, Joseph Lyon, The Descendants of Capt. Thomas Carter of Barford, Lancaster County, Virginia, Richmond, Virginia: Whittet and Shepperson Printers (1912), 2-11, Heritage Quest (Digital Library).
3 Roberts, Gary Boyd, The Royal Descents of 600 Immigrants to the American Colonies or the United States, Baltimore: Genealogical Publishing Co. (2008), 267.
4 Roberts, Gary Boyd, comp., Ancestors of American Presidents, Boston: New England Historic Genealogical Society (2009), 428.
5 Seaver, J. Montgomery, Carter Family Records, Philadelphia: American Historical-Genealogical Society (1929), 36, Heritage Quest (Digital Library).
6 Tyler, Lyon G., editor, William and Mary College Quarterly Historical Magazine, Vol. 17, Richmond, Virginia: Whittet and Shepperson (1909), Jan 1909, No. 3, Page 199, JSTOR (Digital Library).
7 Virginia Historical Society, The Virginia Magazine of History and Biography, Volume 43, No. 2, April 1935, 153, JSTOR (Digital Library).
8 Virginia Historical Society, The Virginia Magazine of History and Biography, Volume 67, No. 1, January 1959, Richmond, Virginia: Whittet and Shepperson (1959), 116, JSTOR (Digital Library).
9 Warner, Charles Willard Hoskins, Hoskins of Virginia and Related Families: Hundley, Ware, Roy, Garnett, Waring, Bird, Buckner, Dunbar, Trible . . ., Tappahannock, Virginia: unknown (1971), 405-409, Heritage Quest (Digital Library).
Sources listed for Major Thomas Carter (ca. 1610-1658) [son of John Carter and Bridget Benion]
1 The American Genealogist, New Haven, Connecticut: D. L. Jacobus (issues newer than 5 years not online), 1985, Vol. 61, p. 179, New England Historic Genealogical Society (Online Database).
2 Brogan, Hugh and Charles Mosley, American Presidential Families, New York: Macmillan Publishing Company (1993), 724.
3 Carter, Jeff, Ancestors of Jimmy and Rosalynn Carter, Jefferson, North Carolina: McFarland and Company, Inc. (2012), 9-10, 13, 24-32.
The ones listed on JSTOR can be a bear to locate - let me know if you want me to pull the links for those, for starters.