Can you provide any PDF’s by any chance?

You could do it in Musescore. But the alignment of neumes is bad and they are too small.

If you want the incipits in square notation rather than in modern (although that is unusual), I’m sure that Adobe has something that would allow for you to add the chant as a graphic inside of an existing PDF (we do this with the Gloria Patri of introits sometimes). But I’d just use modern notation for such short parts.

Here are my attempts at arrangements for the Gradual, Tract, Sequence, Sanctus, Benedictus, and Communion antiphon. For the Agnus Dei, I think my best option is Casciolini's setting. Trying to use a less homophonic setting from one of the high renaissance composer would probably require the priest to wait, which doesn't seem appropriate to me for that part of the Mass.

The Communion is meant to be sung alternating as follows: Chant antiphon, psalm verse, polyphonic antiphon, psalm verse, chant antiphon, etc.

Any feedback is appreciated.

Well, the choir really has no say over the length of Communion, and often with funerals you can't even accurately predict the situation beforehand, so it's nice to have something that can be varied in length a lot. If the priest was the only one receiving, I would do something short as to not make him wait after the ablutions. If you're suggesting Communion should not be distributed to the faithful because of the penitential/solemn spirit of the Requiem Mass, I think I would disagree, but it's not really my call to make anyway. I would hope that everyone receiving Communion is offering up that Communion specifically for the soul of the deceased, and so I would consider that justification enough for a long general Communion, even if that wasn't done traditionally.

Well. regarding the music, what would you suggest?

In the case of only the celebrant receiving, I think I would attempt the following:

1. Chant antiphon
2. Chant verse De Profundis
3. Polyphonic antiphon
4. Chant verse Requiem aeterna
5. Chant * Cum sanctis

I calculate that would take just over two minutes. If you start as soon as the celebrant receives the host, you could hopefully finish the music by the time he has finished receiving the precious blood, done ablutions, and read the Communion antiphon. If your priest is fast enough that doing a verse still makes it too long, remove the verse De Profundis and repetition of antiphon. So you either do chant only, or use the polyphony followed by verse Requiem and Cum sanctis.

Requiem Mass composed by Jeffrey Quick. I have nothing bad to say about it, and it's rather inspiring, but I just don't think it's what I'm looking for

Thanks for the mention! Yes, it's not going to be everyone's cuppa, and there's room for all kinds of Requiems. I don't recall seeing a Feroci setting, though I should check again (I wasn't looking for trouble, and doing a whole Mass is a slog.)

This is nicely done, especially considering the freeware aspect. Setting chant is an issue for all of us. Most of what I've done has involved short chunks of Medicean chant, which is pretty easy in Finale. It is possible now to do Solesmes chant in Finale 27, but it's a pain, and not totally beautiful. It's easier to do it in Gregorio and paste it in, but then you have the issue of matching staff heights. If your program won't include graphics, Acrobat would be your best bet, but that requires access to Acrobat (which isn't cheap).