Sponsa,

I've much experience with this so, while some of what I'm about to write is anecdotal, it's not without an ecclesiastical foundation.

Foundations:
1) Because it's the feast of St. Joseph, the Lenten restrictions on organ music are shelved.
2) The organ has a distinct role to play at Mass. It's not merely an instrument to accompany the choir or the assembled faithful not in the choir.
3) Pope Benedict XVI noted that the old practice was to sing the Sanctus and Benedictus together before the consecration, if they were a unified chant setting, but to divide them if they were polyphonic.

Anecdotal:

1) I've seen a motet sung after the Sanctus, before the consecration.
2) Where I play (at an ICKSP apostolate) there is reluctance (because it's an Institute-wide reluctance) to suppress the organ more than absolutely necessary. Unlike the Irish priests of legend in this country, who deprecated High Mass and multiplied Low Mass on what may have seemed like an exponential curve, the Institute doesn't multiply Low Mass as a goal, only as an occasional necessity. So, I'm encouraged at Low Mass w/ organ to play at the times you describe.
3) The music I play during Low Mass w/ organ is mostly, but not exclusively, a presentation of some part of the Propers for the day, or the appropriate Ordinary. I have some training in improvisation, so that expands what I can do with the melodies I have to work with. I will also include (for example) parts of the Lauda Sion, or the Dies Irae.
4. I tend to think that music which meanders aimlessly doesn't belong in the places you describe, so with a little practice one can learn how much time is necessary, and plan accordingly.

I don't have anything of real worth to say, other than I understand the confusion and agree with you. I absolutely dislike organ music after the consecration. Improvisation or not. Those who support the traditional Mass like to tout its relative (to the Novus Ordo) silence - yes, agreed, and let's keep it that way for the moments following one of the most profound, important things on this earth.

I don't know if this is the issue or not for you, Sponsa, but due to my lifelong study of music and degree in it, when I hear music I can very, very rarely ignore it. If there is random tinkling on the organ after the consecration, my mind goes right to the music, analyzing it in various ways and definitely taking my mind away from what just happened. It is profoundly annoying and I was very upset the first time I experienced it. "Overreaction!", you might say. Okay, fine. But I am not the only one distracted by seemingly random music at Mass. The chants of the Mass are a different story (though listening to/singing those presents its own difficulties to my musical ear).

I understand that such music after the consecration doesn't bother everyone, and that it could even help some.

I have heard plenty of organ music, some glorious organ music. I agree with the Church in that it is the best instrument other than the human voice. But many times -especially accompanying chant, and when it is seen as something to cover any possible silence - it seems very overrated/overemphasized. People need to learn to appreciate chant for what it is in and of itself, and people especially need to learn to appreciate silence when it naturally occurs in the Roman Rite.

I don't know if this is the issue or not for you, Sponsa, but due to my lifelong study of music and degree in it, when I hear music I can very, very rarely ignore it.

So true! There is no such thing as background music and I hear every note of it. It has to be something I learned in music school.

Where I play (at an ICKSP apostolate) there is reluctance (because it's an Institute-wide reluctance) to suppress the organ more than absolutely necessary.

That's one of my favorite things about the way that they celebrate the offices. I have come to look forward to the fanfare on Holy Thursday played before the priest sits (it's technically supposed to end when he finishes at the altar, but it's easier to give the organist ten seconds just in case) in many apostolates, after which the organ is immediately shut off.

De Musica Sacra is basically ignored by the ICRSP and, to be honest, the French in general. They were already doing dialogue Masses and didn't need rubrics, as they have their own customs. The places where I have been don't join the Pater Noster, even the most open to saying more parts of the Mass, for example, even though DMS sort of insists on saying the Pater, despite fifteen centuries of the priest alone saying it. They also recognize that if you suppress the organ more than necessary, it doesn't make silencing it particularly special…

Also, the rubrics from 1908 to 1957 were to separate the Sanctus and Benedictus even when chanted. I find that this is much better, and since I've encountered a fair number of congregations in the US with the absurd custom of kneeling for the Sanctus on Sundays, feasts, and Masses which are not said on weekdays of Advent, Lent, or on the Ember days and are not for the dead (instead of after or, if you divide the texts, at the Hanc igitur or even Qui pridie), I'm not terribly inclined to sing both texts together as some hard-and-fast rule.

I prefer low Mass with organ on Sundays, feasts (in addition to the sung Mass, of course), and when it's allowed (First Friday, etc. — basically, if it's not a Requiem or you would pull out folded chasubles under the old rubrics, you can use the organ for solo music). Obviously, it's somewhat cumbersome during the week, but I've been to parishes where the quiet parts of the NOM have organ in lieu of singing, so it's not a dead concept even with the caveat that there's much less time to play.

This said, I've never run into anyone who plays during the consecration, and if you go to the seminary FB page for the ICRSP (the page is under the Latin name), you can see that they do tone the organ down greatly for the Divine Office, to a somewhat surprising extent. Écône has a much heavier accompaniment. I like both, and the former is obviously due to the influence of Fontgombault on the ICRSP's approach to chant.

It is absolutely not tinkering to fill silence, and it is very helpful to maintain the correct atmosphere of silent meditation even though yes, paradoxically, there is sound. Maybe that's a fantastically modern idea, but here we are, stuck with the ideas of Modern Man™. In any case, I distinctly remember that the coffers for the organ donations magically filled up in four months, from July 2016 to October, in order to allow for the initial restoration of the Wicks organ (now replaced as many here know) of St Francis de Sales Oratory, when periods such as Holy Communion had no Latin hymns or motets planned in lieu of playing the organ.

Playing an “Elevation” (i.e. after the Consecration) is how I was taught to play the EF, and is pretty universal, in my experience, in the Cincinnati metro.

Ruffled some feathers up here (MN) when I did it (as I said, not realizing it would be seen as weird) so I don’t do it here anymore, unless requested by the celebrant. I miss it.

Since I’m used to it, when it isn’t done all I hear is the “silence” of the babies screaming, pews banging, and all the other things a beautiful Elevation politely covers up.

There is (maybe was? recording from 2005) a curious-to-me practice at Westminster Cathedral. NO Mass. Priest sings the Canon, unaccompanied. At "Qui pridie..." the organ comes in, and accompanies him very softly, and then improvises at the elevations; it then drops out at "Mysterium fidei", and rests for a while, until accompanying "per ipsum...." in a similar way.
https://youtu.be/jQmOmXrtmqw?t=2642

The laptop I am using has appalling sound so I can't verify but that Westminster Cathedral practice would presumably be functional, to keep concelebrants on the same pitch.

I couldn't imagine doing what they're doing at Westminster: If for no other reason than the impracticality of trying to decide whether it would be better to start in A or A-flat when the celebrant is singing the quarter-tone between them; or trying to find where the pitch actually slid to by the time he gets to Per ipsum.

Gamba,

You didn't use purple, but that sounds sarcastic. Did I understand?

Yes, of course I jest :)

However, I have known organs where the choir celeste (flat) and the swell celeste (sharp) were well nigh a quarter-tone apart when the temperature wasn't quite right....