If the priest celebrant chants "The mystery of faith/Mysterium fidei" and the doxology using the tones in the Roman Missal, then it is very easy for the assembly to respond with the sung acclamation, "We proclaim your Death, O Lord/Mortem tuuam...," and, "Amen," also using the Missal's tones and without instrumental accompaniment.

When sung like that, those sung moments flow beautifully and are integrated with the entire Eucharistic Prayer.

At my parish, regardless of what other musical Mass setting we are using, the memorial acclamation and amen are always sung unaccompanied using the tones in the Roman Missal, and the priest always chants the Missal's tones that lead seamlessly into those sung responses. The assembly sings them quite well, too.

The problem you describe occurs when a musical setting is used that requires an instrumental introduction of 1-2 measures to indicate pitch, tempo, and rhythm before the communal singing can begin, as is the case with almost all commercially published Mass settings. In such cases, the memorial acclamation and amen do sound like interruptions in the prayer -- because in those cases they are -- and they have all the musical appeal of a toothpaste commercial jingle.

The problem you describe is not due to a structural flaw in the reformed Mass. Poor music choices by the music director and terrible commercially published Mass settings are to blame.

If a music director approaches planning liturgical music with consideration for smooth musical flow in sung prayer, and with consideration for the musical shape of the Mass, then the weakness you describe is easily avoided by steering clear of almost all commercially published settings of the memorial acclamation and the amen.

Mark is right, the only reasonable way to approach these is with the missal chants. It still feels like a gratuitous “the plebeians must now participate” moment tho.

There's been no problem with the Amen in my experience.

The MemAcc suffers from the fact that, if there is no program, there's uncertainty about WHICH text will be used, which invites tentativeness rather than ritual habit. I wouldn't miss it....

“Christ has died…” was arguably the most popular acclamation prior to the implementation of the current Missal.

For myself, I think that's a terrible one. It's not in the official text. Christ has just become present on the altar, yet people say: Christ has died, Christ is risen, Christ will come again. - Is Christ not right there on the altar?

Dixit, I think that was part of the issue with that acclamation. First, it snuck into the Mass without any real pushback, like a lot of things in that era. Second, as you said, it shifted the prayer from second to third person, which didn’t make sense.

That said, I know it was the “go-to” acclamation at least in the parishes around me at the time. I have to say my home parish almost exclusively used that acclamation.

I think what MarkB said makes a lot of sense.

is exactly that same acclamation,

No, one's in the 2nd person (the voice one uses when one speaks to someone who's present) but the other's in the 3rd person (frequently used to speak about somebody). An important 'clue' to the vocative case (2nd person) is the “O Lord” part. We proclaim Your death, O Lord…

Yes, still there
Only in Ireland 4. My Lord and my God.

We use the missal chants, accompanied. I try to use “We proclaim” for the majority of Masses, “When we eat” when the texts of the Mass reflect a Eucharistic nature (such as the weeks of the “Bread of Life” discourse, and on Holy Thursday), and “Save us” for the Lenten season. Also, I hold the accompanying chord for a pulse before starting the chant, and hold the first word slightly just as an encouragement for greater ease of participation.

Also, the priest chants the entire Eucharistic prayer.

At my parish, regardless of what other musical Mass setting we are using, the memorial acclamation and amen are always sung unaccompanied using the tones in the Roman Missal, and the priest always chants the Missal's tones that lead seamlessly into those sung responses. The assembly sings them quite well, too.

Ditto. One of the first things I did when I arrived here was strip the awkward acclamations and accompanied “great amen”. 8 months later, everyone sings the missal responses well.

They flow very naturally in the moment. Instrumental / protracted ones dont.

The singular exception to this is if you have a mass setting that is evocative of chant, and you give the priest the pitch subtly as he begins his part, such that the response with organ flows immediately without introduction in the same key. It’s the same concept as incipits for the Gloria, for instance. If you can set a key and then just flow immediately after the incipit, it works. Barring this delicate arrangement with a competent priest, anything but the missal chants feels like an intrusion to the prayers of consecration, frankly.

Advent/Christmastide: We proclaim your death, O Lord, and profess your resurrection until you come again.
Paschaltide (Lent/Eastertide): Save us, Savior of the world, for by your cross and resurrection you have set us free.
Ordinary Time: When we eat this bread and drink this cup, we proclaim your death, O Lord, until you come again.

Ditto.