It is not as if there has not been effort to claim Nathan Fay 1760-1838 as a Patriot.
The first source that indicated Nathan was a Patriot is in OPF (Orlin P Fay family genealogy) that states Nathan was a drummer in the Revolutionary War 1777. This refers to the Battle at Bennington and Aug 16, 1777 when his father, John Fay, fell as a hero. Nathan was 17 at the time.
Your post is the first reference I have encountered that promotes the idea, adds information and may be able to substantiate claiming Nathan Fay as a Patriot. Both his father, John 1737-1777, and grandfather, Stephen are Patriots and can add support a DAR application. However the information you refer may be needed to substantiate Nathan as a Patriot. Most certainly I would appreciate documentation.
The children of Nathan you mention compare to Nathan's verified genealogy. Nathan married Mary Safford who was the daughter of Gen Samuel & Mary (Lawrence) Safford. Mary Fay (Polly), daughter of Nathan Fay, married Eli Bronson. He was a lawyer and judge of the county (Chittenden) court and representative in legislature. John was a lawyer. Jonas and Truman were respected leaders in the Richmond, Chittenden County, VT region; Truman inherited much of his father's land and business. This is to say the credibility of the deposers may have been the deciding factor behind pension approval.
Currently I am tracing Truman's line to CA and have made new contacts and rekindled old contacts with direct descendants of Nathan Fay 1760-1838. I believe they may be more than happy to consider the proposition of claiming Nathan Fay as a Patriot through DAR or SAR.
Personally I have claimed his father, John, and grandfather, Stephen with the DAR. My direct ancestor is Henry Fisk Fay b 1770 who was but 7 years old when his family fought in the Revolutionary War and a small boy when he lost his father, mother, and two siblings from the war and the impact of the war. Nathan, his elder brother, forever took Henry under his wing and promoted his fortune like a father. I have followed Nathan's ancestors as much as my own as a result and share information with them.
Thank you for the offer to send documentation; may I now take you up on the offer? My email is email@example.com I appreciate your generosity.