Why we sing the Gloria after receiving the Sacrament

Below, a footnote in a Torrance Kirby article on Peter Vermigli's Epistle to the Princess Elizabeth, on her accession.  Kirby here powerfully emphasises how the repositioning of the Gloria in 1552/1559/1662 (a position retained in PECUSA 1928, the Scottish Communion Office 1929, and Canada 1962) embodies the rich Reformed eucharistic theology.  Our hearts lifted up, receiving the outward and visible signs, we partake of the Crucified and Risen Lord ("the internal substance of the sacrament is conjoined with the visible signs"- Calvin).  Thus having communion with "Angels and Archangels, and with all the company of heaven", who gaze "upon a Lamb as it had been slain" (Revelation 5:6), we then join in their hymn:

Important theological significance is attached to the re-positioning of this hymn in the revised liturgies of 1552 and 1559. It is arguable that this liturgical alteration reflects Vermigli’s own substantive contribution to the revised theology of a Sacramentarian “real presence” based upon his celebrated disputation on the Eucharist held at Oxford in 1549. According to Vermigli’s theology of “instrumental realism” participants in the eucharist would be enabled to “sing the song of the angels” only after they had “participated” the body and blood of Christ, hence the liturgical repositioning of the Gloria.

It is interesting that Vermigli's understanding is echoed in Sparrow:

And if ever we be fit to sing this Angels song, it is then, when we draw nearest to the estate of Angels, namely, at the receiving of the Sacrament.

Rather, then, than being an odd, eccentric liturgical practice, rather randomly chosen by Cranmer as a convenient place to squeeze in the Gloria, its positioning in the Prayer Book tradition is a deeply theological statement, indicating the reality of our participation, through the sacrament, in the Crucified, Risen and Ascended Lord.