Use the mass parts as mass parts. There is nothing to hinder you from singing a polyphonic mass in the OF.

I would never advise using the Mass parts as motets.
You can definitely use them where they belong, but be aware that unless your congregation is very musically-appreciative, it is rather awkward for them to stand around and wait for the kyrie/sanctus/agnus/whatever to be finished.

Use an Entrance Hymn, sing all the responses, sing the Our Father/Pater Noster.

I find that having say the Kyrie and Agnus Dei sing by the Choir having the Gloria sung with the congregation and the Sanctus chanted finds you a happy compromise.

Another way is to use a simple chant for the Kyrie, Choir sings Gloria, Sanctus is congregational and Agnus Dei is choir.

Mix it up. As long as you get sung responses, and a couple of other items such as the our Father an an entrance hymn sung by the congregation, you can get away with almost anything from the choir.

Because of the length of the Sanctus and Benedictus and the assumption that they are now sung together, rather than separately and the assumption that the canon must be said allowed, I would avoid using them during an OF Mass, unless you have a congregation that is used to a silent canon and a split Sanctus/Benedictus (and I've only ever seen one OF congregation that is used to that)....but perhaps that tradition will return in the future. All the rest of the polyphonic Mass is perfectly acceptable and encouraged!

We sometimes do an Agnus instead of "Behold the Lamb of God" on OT2 and an Sanctus on OT5 instead of "Twas in the year that King Uzziah died". Complete ordinaries are saved for weeknights; we've done Mozart's Requiem on All Souls and Victoria's O quam gloriosam on All Saints. We have Hassler masses in the files and I'm told the congregation used to join in during Christmastide: maybe I should see if they'll latch onto Lasso's Missa Iager.

Thank you for all of your suggestions. This gives me a lot to think about.

I hesitate to learn a polyphonic Mass for our OF Masses because it would be awkward in our situation to have the choir sing by itself for this long a period of time. Our parish priest is encouraging the Gregorian Masses, so the congregation is already not singing these very much, but the polyphonic ones are even longer, so this may cause some frustration.

I like the idea of mixing it up. I will approach Father with this concept. I think the congregation perfers to sing the Gloria instead of listening to it out of all of the Mass parts.

The singing of responses by the congregation is not yet going well at our church. This is something to strive towards.

The problem, (or maybe not!) is that our parish priest has been offering the EF Mass occasionally! So I would like to learn a polyphonic Mass for these occasions, but I would like to use them more often as well.

I don't see how singing part of the ordinary outside it's place is appropriate. It's like singing a lovely responsorial psalm during the offertory.
It's out of place. "alius cantus optus" does not mean subbing another part of the mass, no matter how beautiful it is.

With respect, Noel, neither argument convinces me.

Again, I understand that people want to go with beauty. I applaud that desire. But we have been given a context, a set form of development in our public (mass) prayers, and that means the mass is more than a pastiche of beauty. The sacred liturgy has it's own musical shape, and unfolds in a sensible and familiar way.

Why would we tinker with that by pretending parts of the ordinary are stand alone motets?

Also, removing or duplicating a part of the ordinary and praying it elsewhere goes against the sensus fidelium. Because the place of the ordinary is so familiar- so ordinary- to the faithful, singing a Gloria or Credo or other ordinary part outside it's designated place would be odd to the faithful. It's confusing.

Noel, please tell me in which book I may find that explicit recommendation by then Cardinal Ratzinger? I believe you, but I've read all his written thoughts on sacred liturgy and I just don't remmeber that.
Also, are we just talking about the Agnus being repeated as a communion motet, or is it a more general idea of using ordinary parts as motets?
To answer your last question- no, it wouldn't make sense. The congregation would be used to the occasional polyphonic setting, so singing parts of the ordinary in their place wouldn't be an issue. It would be incorrect to sing them as motets, because they are in fact not motets.

Bummer- I was hoping for an actual book title.

Thanks Chonak. I'm reading the first link and found the part about the practice of the Regensburg cathedral and the Agnus Dei. I find it odd and problematic, especially as concerns singing through ? the "Ecce Agnus Deii..." and the explicit rubric in the OF that the communion chant begin as the celebrant is communicating, but interesting...
If one accepts the Agnus Dei being continued during communion, does that mean polyphonic ordinary parts are interchangable with motets? Thought provoking.