The Elias Briggs of whom you write was born in VA. His wife Jane was born KY. If he's a cousin of the NC Briggs clan, someone has to establish the link. The son of Elias, Adam is in the 1880 census and confirms this information. My understanding of James Briggs Sr./Anna Collins' or Jr./Unknown wife's children excludes Elias as a son of either. Neither were born in the years you mentioned. There may have been multiple Briggs lines there.
There were two Grady lines in Brown/Adams. One from NC and one from VA, apparently unrelated, and cruelly for researchers living very close to each other at one time. A child of each married and this supports the distance of relationship.