I know this thread is old now, however I have now started to investigate this family myself and would be quite interested in finding out if any DNA testing has been done and uploaded to GEDMatch.com.
I recently came across a GEDMatch test on WikiTree that I shared DNA with, and they descended from this very line of Tobermore Bradley's. What makes it all the more curious for me is that my great-great grandmother's brother, Joseph, was one of the witnesses in William Bradley's wedding (he was Lizzie's brother). Thus I believe that either a Bradley married into my lineage (maybe even a forebear) or a sibling of one my forebears married into the Bradley's.