Well, if you do find the descendants of this Taintor/Tainter line you will have the history & know why the "West" name was used in the middle name of one son of Charles & Mary (Duryee) Taintor. I did find the baptism of your Mary Duryee in NY, but assumed you already have the inf.Good luck on finding descendants of Charles & Mary!
Giles Taintor born July 1802 married Mary Nowell West of Boston, Mass, May 1836.So, Mary (Duryee) Taintor named one son after his grandmother Tainter.
They had: Frank Lathrop Taintor , born Windham, Conn. in 1837 Charles, born March 1840.Married Mary Duryee. Abby Louise, born March 1841 Henry Sherman, born April 1842