See this summary at Anglican Eucharistic Theology. It was certainly a providential turn of events, in my humble estimation, when the Scottish Eucharistic rite made it's way into the American prayer book. As this article notes, "The insertion of these ten words in effect undid Cranmer's (Calvinistic) theology that the sacrifice of praise and thanksgiving was restricted to words and sentiments in prayer." From the article's summary paragraphs:
The Scottish Communion Office of 1764 presents a moderate realist view of both eucharistic presence and sacrifice. The sign is associated with the signified in terms of both the eucharistic offering and the eucharistic presence of Christ. Moderate realism is affirmed throughout the liturgy.
The influence of The Scottish Communion Office of 1764 has been substantial in Anglican liturgical development. Ronald Jasper argues that the 1764 liturgy “marked a watershed in Anglican liturgical history” (Jasper, 1989: 36) since it gave approval to liturgical services based on primitive models. This development has come to be the norm in modern liturgical development. The 1764 liturgy also marked the beginning of a new family of eucharistic rites based more on the model of the 1549 BCP, rather than the 1662 BCP. This idea of different families of eucharisitic liturgies based on either the model of 1549 or 1662 has also been affirmed by Massey Shepherd (1955) and Jasper and Cuming (1987) who along with Ronald Jasper argue that some provinces of the Anglican Communion (e.g. the United States of America, the Episcopal Church of Scotland and the Anglican Church of Southern Africa) follow the 1549 model, while others (e.g. the Church of England, the Anglican Church of Australia and the Church of Ireland) have traditionally followed the 1662 model. In recent times many of these differences have begun to disappear with provinces such as Australia and England adopting liturgies based on more primitive models and reflecting 1549 (e.g. A Prayer Book for Australia, 1995 and Common Worship, 2000). A process of liturgical convergence has occurred throughout the Anglican Communion, with the 1764 Scottish Communion Office remaining a seminal influence and watershed in this development.