John, I think you're right. Nathan, William, George and others were the older children.
In addition to your list of children for David, I also have
Asbury Price, David P. and Alice.
You probably know that David along with his brothers, George
Washington (the 28th), William (Home
Guard) and Benjamin (died in service) were in the Civil War. I'll attach a file (2 pages) that describes David's service.
My line is through George
Washington and most of my research has focused there.