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To add a little more to the picture, Bryan Edwards (Charlotte's father), was left fatherless at 13 when his father died in 1756; the seven children and their mother were rescued by the mother's brothers, Zachary and Nathaniel Bayly, who were both slave owners and sugar planters in Jamaica. It was to  Zachary in Jamaica that the young lad from Westbury went, and it was from Zachary that he inherited plantations.
Edwards' experiences were not unusual, and a similar tale is regaled by Mario Valdes in 'Duff House and its Jamaican Secret' in Historic Scotland, Autumn 2012 pp26-29.

meanwhile I will keep digging for info on the woman with whom he formed some sort of relationship; I await the docs from Kew that I ordered a while ago.
Thanks for your assistance.

 Charlotte's father, Bryan Edwards, refers to her as his daughter in his will, and in this (in 1800) he left her £2000. She was born in Jamaica 2 years before he returned to England in 1774.

Unlike other wills of white men I have read, who had similar 'relationships' (though we can rarely be sure whether the term 'relationship' accurately covers the nature of their unions) with women in Jamaica during this period, of whom there were many, in his will, Edwards never specified the ethnicity of Elizabeth Gaverick, later Nicolle; it was her illegitimacy that labelled her and she evidently carried the stigma of this to her grave - as indicated by the info you refer to on the NA website.
It is likely that she was of both white and black heritage, a combination that, over  succeeding generations, depending who she had relationships with, may have resulted in her being an ostensibly black person with a paler skin tone or an ostensibly white person with a darker skin tone.
One such family I have looked at has produced children whose skins are pale but their heritage from Africa has produced decidedly wiry hair. 

The Dix who Charlotte married was Edward Dix RN, and their son Edward appears to have married Martha Dix, who, as a daughter of the Rev Joshua Dix, was his cousin. This I assume is your line of descent, as Charlotte's daughter had no children. 
thanks for your response