My research has centered on Cherokee connections, so my experience of regular genealogy has been miminal.Since James Bigby,Sr. was born in 1778 in Georgia in the area controlled by the Chickamaugas during the Revolutionary War, it is likely that his white father (Samuel Bigby?) was a supporter of King George III.
I have a copy of a letter written in 1779 by Indian trader Robert Dews to British agent Alexander Cameron which mentions the names of a number of white men (Tories) who lived among the Cherokees and were joining war parties of Indians attacking the American frontier. Although no one named Bigby was mentioned, the men who were listed may have been progenitors of surnames of many Cherokee mixed-blood familes (many names show up in Emmet Starr's HISTORY OF THE CHEROKEE INDIANS). One of the names was [Nathan] Hicks, whose 1/2 blood daughter (name unknown) was the mother of James Bigby. This 1779 letter is posted as part of Jim Hicks Cherokee Website (I don't have the URL at hand).
The Loyalist connections with the Cherokees has been neglected as research.For instance, the Col. Thomas Waters mentioned in your posting was the husband of a 1/2 blood Cherokee woman Sarah Hughes, who was the aunt of the celebrated Chief James Vann. Waters was pardoned after the war by the Georgia legislature, but went back to England. Waters's son George Morgan Waters was one of the wealthiest persons listed in the 1835 Census of Cherokees.