According to the VRs of Rhode Island (''Vital Record of Rhode Island, 1636-1859: A family Register for the people'' by James N. Arnold; Providence [Rhode Island] : Narragansett Historical, 1891-1912) Vol. 2, Kent, Page 91) George's father, James Lewis "Pulman", was born on 17 July 1800 in West Greenwich, Kent, Rhode Island, the son of Psalter Pulman and his wife Elizabeth. That differs from the date you have for him. Also, he had a brother John, born same place on 27 Sept 1796.
Elizabeth Lewis and Psalter Pulman were married at West Greenwich on 19 Feb 1795. (Same reference, Page 33).
There are lots of old Massachusetts and Rhode Island ancestors behind him, so it should be easy to connect him.