Originally there were two Universalist convention bodies, but the Philadelphia Convention died no later than 1809. It was the New England Convention that eventually developed into the Universalist Church of America, and that was what consolidated with the American Unitarian Association to form the Unitarian Universalist Association.
So, if the Philadelphia Convention (1790-1809) was an ecclesiastic dead-end, then why was its Articles of Faith and Plan of Church Government cited and reprinted? Antiquarian interest?
Richard Eddy comes to the rescue in his Universalism in America (vol 2, p. 432).
it’s because the Philadelphia plan was adopted by the New England Convention in 1794, and later adapted or amplified by the meeting at Winchester, N.H. in 1803. That 1794 meeting was the one where Ballou was famously ordained by Elhanan Winchester, with a bible pushed into his chest.