Researching the matter further, I came across Livington's personal Thirty Nine Articles on religion which again slammed the Athanasian creed (and thereby the Trinity). Those and Livington's other writings found in the Independent Reflector can be found in this book.
Unfortunately, google books blocks important parts of Livingston's writings and the entire Thirty Nine Articles haven't yet been uploaded to the public domain provisions of the Internet.
So I went to the David Library in Washington's Crossing and researched them. Unfortunately, the microfilm copies I made don't read well enough for me to post them (for now). But, the good news is I read the entire articles and you will just have to trust my honesty and independent verification of the record.
The articles are a brilliant satire against the notion of "orthodoxy" or "religious correctness." Among other things, the articles chiefly target ecclesiastical authority, Roman Catholic doctrine, the Thirty Nine Articles of Faith of the Anglican Church, and the concept of orthodox Trinitarianism itself. Nowhere in the articles is the Trinity and cognate orthodox doctrines defended. The 39th Article of Livingston's Creed reads:
I Believe, that this Creed is more intelligible than that of St. Athanasius; and that there will be no Necessity for any Bishop to write an Exposition on the Thirty Nine Articles of my faith.
In Livingston's Thirty Nine Articles we see an important but not too well understood zeitgeist of America's founding era "Protestant Christianity." It's where Roman Catholicism and ecclesiastical authority are so suspect that doctrines like original sin, trinity, and even the "right" (that is the traditional) books and copy of the biblical canon become associated with such and, consequently, are written off as human corruptions.
The Quakers, as it were, who lack ecclesiastical authority and creeds become the most authentic expression of "Christianity," except for their theological refusal to take up arms against political tyranny.
And yes, that is expressed in Livingston's creed: See Article VI.