It does appear that the wrong Elizabeth Woodward is attached to "Unknown" Lincoln, you are right. Elizabeth Woodward, daughter of Israel Woodward married Robert Taft, it appears. I have not found anything showing she married anyne named Lincoln (yet). I suspect you are right that "Unknown" should be Samuel, but before his name is changed I'd like to find vital record-type sources.
It looks as if Elizabeth Woodward, daughter of Nathaniel does not have a profile yet; I will create it.