I got a reply from an Old Rite priest and he tells me that the Old Believer text for the Liturgy does not have the prayer in question: "Wash away, O Lord..." My guess is, then, that its inclusion by the ACROD would reflect a liturgical development in the same direction as the rest of Orthodoxy.
I am still puzzled why the Melkite text omits this while the Antiochian text retains it. It seems hard to believe that the prayer developed after the Schism between the Antiochian Churches in the early 18th century. I think there's still something missing in fully understanding this variation in the liturgical texts.
David Ignatius DTBrown@aol.com