You are correct. "My Joseph", born 1766, died 1851, is not a son of Hezekiah as was long thought. I have found many cousins who entered the DAR based on this incorrect information. They could have qualified through Elizabeth McReynolds, Joseph's wife, or through his recently identified ancestry.
In my searches, particularly for a living male line descendant of Joseph for DNA testing, which we found, I have identified many cousins.
The story of the search for Joseph's parents is very interesting. I have letters on this subject which go back over 100 years.
Elizabeth McReynolds was the daughter of Joseph M McReynolds and Mary Margaret Mitchell.
Joseph is descended from Joseph, dates unknown, through one of his sons, James, 1740-1799.
If I can help further, please let me know.