I believe they moved to Mass in 1831/2 since John (1830) is listed as born in NJ and the others, starting 1833, are listed as born in MA.
I have census and Boston registry info from 1830 to now. Also headstone pictures for Henry (1806) and Margaret Hawthorne (1804) and the children you listed up to my father.
Were you able to open the link to the baptismal list at Totowa church? That is the wall I am against now.