I have posted the communion service of Fredric Henry Hedge, from his 1853 Christian Liturgy: For the Use of the Church, as a resource page. You can find it and others in the menu from the main page; I intend to post other items in time.
Properly speaking, it is the anaphora, or as Hedge puts it "the concluding or cenatory act. In a service so liable to excess of formality, it was judged best to leave a wide margin for such voluntary exercises or such spontaneous expressions of thought and devotion as the Minister or Church may be moved to connect with it."
I wouldn't expect anyone to use it today as-is. For one thing, it has phrasings — such as dumb for unable to speak — that reasonable people would find offensive. To tell the truth, I wonder how often it was used then. But it was a source for other Unitarian liturgies (and Universalist, as they seemed to borrow heavily from the Unitarians) particularly via the work of James Martineau.
Or so I think. I've never traced out the influences, and liturgical primitivism was in the air. But that's a future project to prove or refute.