I don't find a Stephen in this book, but this is my go-to guide for the Burwell family. I am a descendant of the Burwell family through 3 lines.http://books.google.com/books?id=e1VlAAAAMAAJ&pg=PA94&am...
You can download the free PDF for easy viewing offline.
It is likely Stephen is a descendant of one of these lines. There was only one Burwell family.
Good luck in your search.