No DNA work that I know of.
The David Garrison that you speak of did have son Jasper Newton Garrison - he is my great great grandfather!
Divid also had a son named James. James died of phenomena in the Civil War. Jasper had many children. His oldest son John Henry was my great grandfather. Jasper's third son was JAMES MADISON GARRISON, b. November 29, 1859, Georgia; d. August 15, 1926.
So you are right, there is a connection. I have lots more info if you would like. Contact me at firstname.lastname@example.org