I have been doing genealogy < 2 years.I just now learned of the Mayflower connection thru Lucy Carr, 2nd wife of William T. Winter. I recently found their graves in Brown County, OH (about 70 miles from my home). William is buried with his last wife, Malinda Patten, but next to Lucy. I have a copy of their wedding application in December 16, 1852 and their death records.
You mentioned the Walker family. Are you perchance descended from Franklin Pierce Walker and Harriet Winter? As a child, my mother knew them. We come from Margaret Charlotte Walker, their oldest child.
I have traced the Walkers only back to John W. (b. 1821), but I have found a lot of his descendants. I've traced the Winters to Mordecai (b. 1740). I'd love to see a picture of William T. Winter.