I'm not aware of any examples, but that could be an interesting project: perhaps to start with some existing antiphon with organ accompaniment, and add fauxbourdon verses in the appropriate mode.

Although not exactly what you are looking for, but might it be useful, if I make an edition with the Latin (instead of English) Doxology of my three part Anglican Chant?

As the formula can be used with any psalm verse, underlaying a specific chant would be pointless. So you would still have to mark the chord changes in the psalm verses somehow (asterisk, underline, ...), but at least the (through-composed) doxology would be written out.

if I make an edition with the Latin (instead of English) Doxology of my three part Anglican Chant?

I think it would be useful, but a score with a complete psalm with the notes corresponding to each word or group of words would be more useful, especially for less experienced choirs, also because doubts may arise about how to accent the Latin words.

Excellent work and very clear score!

@Andrew_Malton To quote from romanliturgy.org:

The Nova Vulgata, or Neo-vulgate, is the Latin translation of the Bible used by the Church in the current editions of the liturgical books.

This does not apply to through-composed traditional pieces like, e.g., the monodic chants in the Graduale, but when the verse is recited on a psalm tone (like in the communion pieces in the Graduale), the Nova Vulgata should be used, I think. It is also used in this context in newer editions of chant books: The Antiphonale Monasticum from 2005, e.g., gives the Magnificat text with "in Deo salvatore meo". The Magnificat is an interesting case, because, although the Nova Vulgata made only very minor changes, the editors took care not to change the number of syllables, so that the text can be exchanged even for through-composed music (of which there is a lot for the Magnificat). Unfortunately, the Nova Vulgata is still copyrighted, which poses problems when it is used in third party publications like musical settings. That's why I have used the old Vulgata.

I find irony in the idea that composers are required to use a copyrighted text.

Quoth @Liam:

Under the #IfTheWorldWere4SomeStrangeReasonToSufferMeAsPope category, one very public agenda item would shifting to a much more widespread norming of the adoption of CreativeCommons-type models for the Church's liturgical and scriptural texts in civil jurisdictions where that is possible.

Were I running for public office (God forbid it!), I'd advocate something even more radical: establish specific legal protections for an author's moral rights (i.e., legal remedies both for plagiarism and for presenting derivative works as the original), and then remove copyright protection from religious texts. You don't need the economic incentive of copyright to foster the creation of religious works, and it's to the benefit of society to prevent religious entities from restricting the distribution of their teachings. (For the latter, take a look at the various legal strategies the Scientologists have used to silence their critics.)