I doubt your James Kendrick is related to the Miramichi Kendrick. On the 1900 census, he is listed as born in Canada English, with both parents born in Pennsylvania.
In Markham Township, York County, Ontario, there is a couple named Samuel and Rosana Kendrick (Kindrick, etc see 1851, 1861 and 1871 census) who are Mennonite from U.S, with a family born in Markham township. They are probably born in Pennsylvania like the other Mennonite around them. Possibly James parents was related to them?
It might be a more likely source than the New Brunswick, etc Kendrick