Barry, On the children of Nathan Perrin and his wife Emily Satterley, I have the following from the 1850 Census for Warsaw Township, Jefferson Co., Pa.
Lucretia, 14 Ephraim, 13 Helen, 8 Hepseba, 2
Lucretia and Ephraim were born in N.Y., the rest in Pa.
I assume the youngest child is actually Hebzibah, since Emily's mother was Hepzibah Barton Satterley.
Regarding the Van Zant connection, that is quite interesting. This is a totally different branch of my family. The Perrins are my maternal grandfather's ancestors and his line is all Pa./N.Y./New England. But my Van Zant line is an unusual branch of my paternal grandfather's otherwise Southern line. DNA testing has recently confirmed that my recorded ancestor Garrett Vanzant of Lincoln Co, N.C. is identical with Garrett Van Zandt, b. abt. 1726, the son of Albertus Van Zandt of New Castle Co., Delaware, who is from the line you mentioned. It had been suspected that DNA would confirm this for some time because of the popularity of Garrett as a name in both families.