Does the GIRM list this option?

This is a matter of the historic methods of psalm singing.
What you are suggesting fits none of the historical paradigms for psalmody.
1. Responsorial, 2. Antiphonal, 3. In directum.
That's not to say you couldn't do it, but that it would be... eccentric.

In responsorial psalmody such as we normally sing at mass (and of which the gradual responsory in the GR is a vestige) the cantor sings the verses (preferably NOT to a mere psalm tone) and the people sing the responsory, sometimes called a respond (NOT the 'antiphon', which doesn't exist in responsorial psalmody).

Actually, while it is common nowadays for the verses to be sung to a psalm tone, they should actually be sung to a chant-like melody more elaborate than the responsory itself.

Yes I understand that it has not been a standard way of using the psalms. That might be because of medieval constraints of illiteracy, and the cost of books. (I may try to expand this thought into something more coherent.) And I don't think we know how psalms were used in the time of Ambrose and Augustine.
Furthermore using psalms at Mass as GS does, and GR now, is not based on any medieval or more recent practice, as far as I know. Cranmer did not adopt it for the Communion, and Matins and Evensong are office antiphonal uses without responsory.

This suggestion was really quite a bit more common than you would think back during the revolution.

It never did catch on much.

My question: does singing a token and formulaic bit of a Gregorian Introit increase the prayerfulness or meaningfulness of the rite to the PiPs?

I don't know of any post-conciliar liturgical legislation of the Roman Catholic Church which refers to the people's part in a responsorial psalm as a "respond." So I wish we would see an end to some persons insisting that we have to call it that. It's a "response." And, actually, in GIRM 61, final paragraph [USA adaptation], there is even a reference to "or an antiphon and Psalm from another collection of Psalms and antiphons..." [emphasis added].

I'm willing to refrain from using "antiphon," in reference to the responsorial psalm, but I will not use the strange "respond."

In regards to "nothing that I have noticed would prohibit" [the OP's suggestion], well, GIRM 61 does permit singing the psalm in directum without a response. It does not specifically state whether the assembly or choir/cantor sings the psalm straight through, but the whole thrust of GIRM 61 is that the people/congregation/assembly be able to take part in the responsorial psalm in some way, so it makes sense that the in directum option ordinarily refers to everyone.

I'm willing to refrain... but I will not...

There was the merest mention that the responsory was 'sometimes called a "respond"' - absent any suggestion that anyone or everyone should call it that. 'Responsory' is quite acceptable. However, the term 'respond', being quite common in academic literature about chant and responsorial psalmody, is hardly 'strange'. I'll be happy if people (especially church musicians!!!) stop calling responsories antiphons.
It's so simple: responsorial psalmody = responsory, antiphonal psalmody = antiphon. The two are not interchangeable. They are quite distinct methods.

Still and all, I quite agree with the tenor of your commentary about in directum performance as a viable option. For that matter, there is no legislation forbidding antiphonal performance of the psalm at mass - in which case there would be an actual antiphon. I have witnessed true antiphonal psalmody by the gospel and epistle sides of the congregation at vespers here in Houston. This was during the tenure of our member Felipe Gasper at Annunciation. Congregations can do quite amazing things under talented leadership and absent those mindless naysayers who love to go about quacking their tiresome refrain - 'Catholics can't do that'.

Fr Columba's Entrance and Communion chants are an innovative type of psalmody in that they have no formal precedent in historic methods of singing either the psalms or the mass propers. This is not intended as a negative criticism, just as a matter of objective fact. I have studied these with him and taught them in workshops which I gave with him. The melodies are his new compositions and are not necessarily based on Gregorian originals. The form unfolds thusly -

Antiphon - a moderately elaborate version for schola
People's 'refrain' - a simple melody and abbreviated text for the congregation
Verses - schola, to a St Meinrad tone
People's 'refrain' -
Verses -
People's 'refrain' -
Verses -
People's 'refrain' -
Antiphon - Schola

This form is followed in father's entrance and communion chants.
The object is to involve the people in the Introit and Communion chants.
As such, this represents a new approach to 'propers', for which there is no precedent in the historical chant repertory. Actually, while there is no antiphonal singing, this represents a sort of hybrid marriage of antiphonal and responsorial psalmody. As always, father's chant compositions are exquisite.

CGZ, you caught my pun. Bravo.

The historical precedent for psalmody in directum in the Mass is the tract.

Good question, Cooze.

The gradual responsory as exampled in LU long ago evolved into a soloistic chant, sung by highly trained soloist(s) and/or an accomplished schola. It is probably best sung in such manner. As such it has ceased, as performed, actually to be responsorial. Its modern counterpart in the NO's psalm responsory is another matter. In fact, as sung, the NO's psalm, as normally performed, represents the very inversion of roles about which you speak, namely, that the people's responsory is normally more elaborate that the paltry psalm tone to which the 'cantor' sings the verses. This is precisely the opposite of the relationship that should inhere in responsorial psalmody. As I have intimated many times here, the verses are what should be sung to more elaborate music, preferably a different melos for each verse. Singing the verses of responsorial psalmody to mere psalm tones is a regrettable and degenerate practice. The psalm tones exist for one purpose only: for large groups of people to sing psalmody in antiphonal or in directum fashion. It is a perversion and a shame for them being used nowadays by would-be cantors in responsorial psalmody.

It seems to me that our LU repertory is not really where one should look for the academically correct performance of responsorial or antiphonal psalmody, for, beautiful as they are (and I would be the last to wish them disused) their method of performance is not always true to that implied by their 'antiphons' and 'responsories'. This is most true of antiphons that are followed by psalmody during Holy Week rites, and even the propers of the mass. Calling a chant an 'antiphon' (unless it is a stand-alone generic chant) implies that any psalmody sung in connexion with it will be sung antiphonally - a thing which, in my experience and knowledge, does not happen. Should we not, for instance, have two groups singing psalm verses antiphonally following the introit, offertory, or communion' antiphons'??? This never happens, and if it did, who would the opposing groups be?

Further, some scholars now hold that the offertory was originally a responsorial form, not the antiphonal form implied by calling its chant an 'antiphon'. There has been no end to things getting changed but their labels remaining unchanged. If these scholars are correct, then the offertory 'antiphon' is actually the offertory 'responsory', the 'responsory' of a responsorial psalm, not the 'antiphon' to an antiphonal psalm. The same may be true of the communion 'antiphon'. Even now, I think, in many places where the propers are sung, the communion psalmody is, in practice, responsorial rather than antiphonal. When that happens we should stop calling things 'antiphons' when the psalm is sung responsorially - we should call them what they are in practice, namely, 'responsories'. (It is beginning to sink in on me, though, that certain types of folks just like to bandy that work 'antiphon' around so as to impress people who don't know any better, not really caring about what it actually means or implies with regard to forms of psalmody.)

Well, check out the Latin edition of the Missale Romanum. That's where "antiphon" comes from!

Bugnini p891: (my emphasis)

The entrance and communion antiphons of the Missal were intended to be recited, not sung, and to inspire the creation of suitable songs in the vernacular

My understanding is that the ban on singing them (which still applies to English speakers outside the USA, AFAIK), was to ensure the continued use of GR (and GS) !

does singing a token and formulaic bit of a Gregorian Introit increase the prayerfulness or meaningfulness of the rite to the PiPs?

Maybe. Are you asking for scientific polling data? Lacking that....

In a near-western suburban parish, the MD has decided to use a (de novo, not Gregorian) psalm-tone introit, offertory, and communion versicle. Although the offertory and communion chants are sung at the right time, the introit precedes the "gathering hymn."

The congregation acts just like a congregation in a more-distant western city (same Diocese) which has--arguably--one of the worst music programs extant and has never, to my knowledge, used ANY of the Propers at any Mass.

There. Science!!

Several above have noted that, as usually practiced, the people's responsory is more elaborate than the cantor's uninspiring and improper psalm tone. This is, indeed, just the opposite of what should transpire. The solution suggested above, I think, does not address the impropriety of the situation as it exists in most places. The people should not be given ever simpler and simpler responsories to sing, but the cantors should be expected to sing verses that are more florid than the responsory.

In other words, stop dumbing people down by giving them easier and easier responsories (some even stoop to the absurdity of making responsories out of butchered psalm tones!). Give them real but quickly learnt musical melody, but expect the cantor to sing somewhat more elaborate and real melody as well.

When, when!, WHEN!, are we Catholics going to stop treating people like morons when it comes to music, stop assuming that they cannot sing or learn decent stuff. Giving them a psalm tone for a responsory, for instance, is a slap in the face which they ought rightly to refuse to sing. And cantors? Anyone who can't do better than to sing a psalm tone responsorial verse, Gregorian or de novo, is not by any stretch of the imagination a cantor at all.

The correct approach is to find (in this order) a) suitable music b) which is in the congregation's ability (their real ability, not what you think they 'can't do'), c) teach it to them without a doubt that they can and will learn it, d) your tutelage of the people should be characterised by an indeflectable assurance and insistence that they are going to learn what, with reasonable effort, they jolly well can learn. Never again catch yourself saying 'Catholics can't', or 'these people can't', and so on. Empower them. Give them permission and invite them to excel. Remember! It isn't so much what the people can do or learn, but what the teacher is competent to teach! In most instances by far, in any situation, it is the teacher who 'can' or 'can't', not the people or the students.

Noel is 200% correct! We have touched on this before on our forum. Taking a due from Anglican experience and custom would not necessarily have meant wholesale mimicry, which would have been just that - a copy cat mass. But! Taking a cue, being guided by basic underlying principals and the God-centred 'beauty of holiness' is another matter which was consciously and with purposeful deliberation eschewed because the gentlemen (and their women friends, religious and all) came home from the council and determined to do what they wished, not what the council had admonished. They emphatically did not wish in any way to take a cue from the Anglicans. They wanted just the sort of abysmal musical and literary drivel that has been pawned off on us and that we will be yet more generations getting rid of. And, we Anglicans are not the only ones to possess a high ritual patrimony. There are, I suspect, similar patrimonies in other ethnicities, and the witness of high Benedictine worship. There was no shortage of historical examples the study of which would have given us a true organic development from our true historical ritual patrimony.

Just to clarify: my question had nothing to do with psalm tones.
I'm talking about a Gregorian gradual (you know, that which follows the epistle and precedes the alleluia), and whether or not it would be OK for the cantors (whose role as unofficial "soloists" is usually ended at the asterisk, but resumed at the verse) to sing the full Gradual, up until the verse, at which time, the "choir" sings the verse of the Gradual (not in psalm tone, but the actual verse of the Gregorian Gradual). Thus, an "inversion of roles." ?

Antiphon - a moderately elaborate version for schola
People's 'refrain' - a simple melody and abbreviated text for the congregation
Verses - schola, to a St Meinrad tone
People's 'refrain' -
Verses -
People's 'refrain' -
Verses -
People's 'refrain' -
Antiphon - Schola

This form is followed in father's entrance and communion chants.
The object is to involve the people in the Introit and Communion chants.
As such, this represents a new approach to 'propers', for which there is no precedent in the historical chant repertory. Actually, while there is no antiphonal singing, this represents a sort of hybrid marriage of antiphonal and responsorial psalmody. As always, father's chant compositions are exquisite.

There is an example of this type of psalmody (Antiphon, response, verses) prescribed in the liturgy of hours (example from the feast of Transfiguration):

Antiphon 3: As they came down from the mountain Jesus commanded them: Tell no one of the vision until the Son of Man has risen from the dead, alleluia.

Canticle - See Timothy 1 3:16
The mystery and glory of Christ
R. Praise the Lord, all you nations.

Christ manifested in the flesh,
Christ justified in the Spirit.

R. Praise the Lord, all you nations.

Christ contemplated by the angels,
Christ proclaimed by the unbelievers.

R. Praise the Lord, all you nations.

Christ believed in throughout the world,
Christ exalted in glory.

R. Praise the Lord, all you nations.

Antiphon 3: As they came down from the mountain Jesus commanded them: Tell no one of the vision until the Son of Man has risen from the dead, alleluia.