William Fosdick - Different William Fosdick?

I contacted the Mayflower Society to confirm this line, since it goes all the way to William Brewster, who came on the Mayflower, and it would have qualified my family for inclusion in the Mayflower Society. They said the William Fosdick who was the son of James Fosdick and Elizabeth Fosdick (Darling) does not appear to have had children. They said this was probably a different William Fosdick. I dug a bit deeper and saw that there is indeed a William Fosdick in the 1810 US Census in Hebron NY area, but his age was listed at 26-45, which means he would have been born in 1765-1784, further suggesting this is a different William Fosdick. Google this to see the 1810 Census entry - "william fosdick" census f232.

If anyone has any other primary sources (e.g., land records, marriage certificates, etc.) to show this is the same William Fosdick it would be great to see, as that is what the Mayflower Society would require to link this line.