What was her date of death? Most Schermerhorns descend from Jacob Janse, immigrant 1664 from Holland. She sounds like her father must have come much more recently than that! So the date would help a lot in determining whether she is part of the earlier family or not.
Try Findagrave.com for either her grave or his.
And try Olivetree.com for ships lists, if you haven't already, in addition to Rootswebs' list--I can't recall exactly the URL, but if you go to the message board and look under "other" you should find it.