Until the mid-1970s, it was assumed that any untexted part in works of Dufay and his contemporaries was played instrumentally. This was less successful than one might imagine, particularly in secular music, because the available string technology and instrument sizes led to dull bass notes in the ranges required. (Organs work a little better.) At about this time, Christopher Page with his group Gothic Voices pioneered all-vocal rendition of this music, in performances so convincing as to itself become an orthodoxy for awhile. Page's arguments were set out primarily in the journal Early Music.

The options for singing these parts are: 1) vocalized on a vowel ; 2) sung on the words of the original tenor chant 3) sung on words taken from the other parts. 4) more than one of the above, in different parts. Contra parts would seem to want more words, but they can be very effective in a scat-like style. In short, there's no cookbook; do what works best for your singers, informed by the best information you can muster.

Me personally? I'm busy with some other projects. But one certainly could do that; it's within the range of what might have been done. Remember that musicologists are not in charge of Purgatory, no matter how fit for that duty some of them might be. And if it got Dufay into the liturgy, I'd assent to fitting David Haas texts to the untexted lines. However, in this case, it's the texted lines that are your real problem; I can't see a liturgical use for a song in praise of Cleophe Malatesta. (If you're talking about concert use, then of course it's not an issue.)

Contrafacta are not dead! Match a 3-part piece with a text that you need liturgically and fit the text in. Last Sunday one of my ensemble was not there so we suddenly needed an ATB motet for offertory - I had one evening to produce one, so I took Pullois' 'Pour Prison' and turned it into "Bonum est confiteri." The first time you do one of these it takes a while, but after doing a few you get better at it. I use these all the time - with no money to hire anyone and a volunteer ensemble consisting of anywhere from 3 to 6 people on a given Sunday, this is a necessary skill (unless you are a Mozart and can compose a complete piece in the twinkling of an eye).

For the contratenor and tenor it is possible to use just a part of the text (since the complete text is in the top voice it is liturgically correct) that makes sense. You can repeat it as well, which is also compatible with isorhythmic thinking. Jeff is right about the various ways to do it (and, BTW, he has sung more than one of ours at Immaculate Conception).

Do you have a specific Sunday in mind when you will use this piece? I would see if one of the propers for that Sunday would fit the music. That would probably be better than trying to salvage bits and pieces of the original non-liturgical text, IMHO.