We continue the examination of the document Ordo Cantus Missae, which forms part of the introduction to the Roman Gradual, the official Roman Catholic book of music. As always, I note the kind contribution of Richard Chonak who translated the Latin original of the second edition (1988). After the Kyrie (or its replacement) comes not a strophic hymn, but a traditional piece cited as a “hymn”::
3. The hymn Gloria in excelsis is begun by the priest, or, if appropriate, by a cantor. It is presented either by a cantor and choir in alternation, or by two choirs responding to one another. The division of verses, marked with a double line in the Graduale Romanum, need not be preserved if a more suitable manner is found that can be combined with the melody.
When the rite of blessing and sprinkling holy water is used in Sunday Masses, this rite takes the place of the penitential act.
Roman practicality at work: the priest-celebrant begins the intonation, but if he is unable, a cantor will.
Perhaps we should be surprised the OCM doesn’t address that bugaboo of many American church musicians, the responsorial Gloria. It does give an alternate method for singing the piece: alternating choirs. More traditional? Perhaps. My own preference is through-sung, with the assembly. As a stepping stone to full participation, I have no problem with phasing in the Gloria, from a choir-only piece to a responsorial form, to a setting sung through by everyone.
Catholic Sensibility 
I prefer sung-through, too, but I have no problem with the middle section being choir/schola only. I don’t have a problem with an occasional choral-only Gloria on very festive occasions when the people have lots of other things to sing and/or there are many visitors (the responsorial Gloria was in practice intended to deal with that latter situation).
But most importantly, it should normally be sung. It’s a hymn; it’s very nature is that it’s supposed to be sung (ditto the Sanctus). If you’re singing an entrance hymn and reciting the Gloria as a regular practice, that’s something that should be fixed.
There is actually a hierarchy of sung music in the Liturgy. The following excellent article describes it in some detail. http://www.ccwatershed.org/blog/2013/may/24/surprise-musical-hierarchy-sttl/
Lots of people have their own take on the hierarchy. I would take exception to a few aspects as explained by Dr Clark and Dr Mahrt. One can turn to the GIRM and to the rubrics of the Ordo Missae to easily see what “hierarchy” is actually embedded in the Missal itself.
The Gloria is a hymn, by genre, and as such is accorded a lower status than antiphons and psalms. But it is also an integral part of the traditional musical Mass setting. Another point of “ambiguity and arguable self-contradiction,” as Dr Clark ascribes?
Also on your link, I would also take exception to the exaltation of Musicam Sacram (1967) as an implementation document above that of not only the GIRM but the Ordo Missae itself. These are the essential lifeblood of music ministry practice. The documents come just after that, once the essence of the Roman Rite is mastered. Do the rites first, study and perceive an understanding later.
Oh, and as with you and Liam, I too prefer the through-composed versions.