The answer may be an artifact in the collection of George Washington Papers at the Library of Congress, 1741-1799: Series 2 Letterbook 24 - Image 251. Although it was written with exceptionally fine penmanship --presumably by a professional scribe for archival purposes-- it was not by the hand of our first president but, it is clearly dated 17th September 1796.
Still, the fact remains that, on 19th September 1896, in observance of the Centenary of this monumental event in our nations history, the predominant newspaper in our nation's capital specifically reported about the matter of the date and should have put to rest any and all uncertainties about it then and there.
What remains a mystery is how it went undetected for so long by so many but, at least now, a viable source of which this error be attributed has been discovered.
ON FACEBOOK: George Washington's Farewell Address