I'm not sure exactly which Josiah Bradshaw you are working on. But here are some things to ponder.
William Bradshaw, who died before 15 Sep 1747 in Goochland Co VA and his wife Judith Scruggs did have a son named Josiah. The proof is in Cumberland County VA Deed Book 1, p 30-38. These are four separate deeds written on the same date (24 Jul 1749) from Field Bradshaw, eldest son of William Bradshaw dec, to Field's brothers Charles, John, and Josiah Bradshaw and their brother in law Field Robinson.
This Josiah Bradshaw was a resident of Bedford Co VA on 25 Feb 1774 when he and his brother William Bradshaw, along with their wives Elizabeth and Susanna, sold part of this same land to John Hobson of Cumberland Co. (Cumberland Co VA Deed Book 5, p 232-233) Elizabeth wife of Josiah and Susannah wife of William had not signed away the dower, so their consent was made on 4 Mar 1774 in Bedford Co and recorded in Cumberland Co Deed Book 5, p 262.
I believe this Josiah Bradshaw in Bedford Co in 1774 is the one who married Elizabeth Armistead in Cumberland Co in 1763.
These Bradshaw profiles are a mess. I wish you luck sorting out the problems.