My wife is a gr-gr-gr-grand-daughter of Alvah Palmateer and his wife Mariah Carey, through their daughter Jane (Jennie) Palmateer. Most of Alvah and Mariah's children settled in either Monroe Co., NY or Sanilac Co., MI, and if you are interested in this family I can fill you in on them. Much of what I have originated with my wife's grandfather, who is still alive, remembers them all, and I have been verifying his knowledge with as much original documentaion as I can find. (I believe Alvah is a son of the William you mentioned).
I have just begun, in ernest, to try and find the link for her Palmateer family to the Palmatier (that is how it is spelled in the States)Family.
In short, I am certain that the line will trace back to Pierre Parmentier who arrived in New Netherlands in the 1660s. Beginning with his son, Michael's generation, the name was more often written as Palmatier (with many variations, Palmentier, Palmontere, Palmetier, Palmeter, etc.) The Palmateer spelling seems to be in favor starting in the 1800s and more often with the Canadian lines. It is rare in the States. An excellent account of Pierre Parmentier can be found in the New York Genealogical and Biographical Record vol.138, nos. 2 & 3 (Apr. & July 2007). Pierre's only known child, Michael Parmentier/Palmatier settled at Poughkeepsie, Dutchess Co., NY around 1700. His descendants mostly remained in the Poughkeepsie area or across the Hudson at Kingston and New Paltz in Ulster Co. through the period of the revolution. I believe I have narrowed down the family from which the Canadian Palmateers descend. However, I am looking to acquire more original or primary documentaion as to the whereabouts of Simon, Francis and William in Northumberland County in order to get a better clue to their ages, when they settled there, and why they may have gone. While I do have access to the 1851 and up Canadian census, I am looking to gain access to the land records, grants and petitions that may pertain to the Palmateers. I live in Orleans County, New York (actually directly across Lake Ontario from Northumberland Co.). Can you direct me as to how I might acquire some of the records you mentioned in your posting?