What do you mean by "the traditional one"? The Kunc? Plainsong? I found a Kunc accompaniment here: https://archive.ccwatershed.org/media/pdfs/15/03/29/01-55-48_0.pdf For the plainsong, I've found a "lead sheet" (melody and chord symbols) on MuseScore: https://musescore.com/song/christus_vincit-6519625?srsltid=AYCX9vKyaiyRK0ZtAe-HDMp0K4hXnab-Hh_zhfk2v_6J2by3QnQF2J0T To answer your first question second, I think it's perfectly fine to accompany it on organ if they need a boost, especially the Kunc. I know others may disagree on organ accompaniment of chant, but I'd rather have it done well with accompaniment than poorly without it.

The Musescore Official one is by Laurence Bévenot and requires $6.99 purchase.
Christus Vincit (Arr. Arranged by Lawrence Bevenot OSB 1901-1991) - Plainchant

There is a free choral Musescore Laudes Regiae but print only, not download mscz at https://musescore.com/user/8551836/scores/12592915

The Laudes Regiae square note PDF at https://scholamalverniensis.chessck.co.uk/api/blobs/site3973?path=Christus%20vincit%20(updated).pdf says "Based upon an original chant transcription by Dom Laurence Bévenot OSB (1901-1990) from Codex F, 160 of the Worcester Antiphoner (13th cent.), first published in Music and Liturgy, October 1940, copyright © Society of Saint Gregory, and in which all rights are reserved. The present edition may be freely copied for non-commercial purposes."

Today I learned "'Christus vincit' is the anthem of the Society of St Gregory, the national society for music and liturgy in England and Wales"

Here's the CCWatershed organ version, no attribution that I can see: https://archive.ccwatershed.org/media/pdfs/15/03/29/01-55-48_0.pdf

And also at the Institute of Christ the King.

P.S. Off topic but this obituary of Laurence Bévenot in the Ampleforth Journal (old insecure http, not a problem) is a most entertaining read.

It reminds me of a Crusader chant, a time in Church history I would not be keen to evoke.

Why not?

The Laudes Regia is fantastic when it's BIG, so organ is not a problem. I'd want more than 2 singers. Hopefully you have big voices. Edit - maybe a good choice to wait until the choir is larger. Ime, even at a congregational-singing-challenged parish, people do pick up the Montani refrain easily.

LR could fit in the TLM offertory if you shaved off a couple of the verses.

Re: history, not a scholar by any margin, but my understanding is that it was patterned off of triumphal litanies for Roman victories, so yes militant is a key word, if that wasn't clear from the text alone.

@trentonjconn the use of Christian endorsement of wars of conquest on the Middle East.
At least that's how I remember it. The real story is, as usual, 'it depends' as discussed in:
https://www.reddit.com/r/Catholicism/comments/158h1uc/how_do_modern_catholics_view_the_crusades/

@roborgelmeister has just provided more insight on its use.

Laudes Regiae (from an Ambrosian Chant) appeared in many editions of The Peoples [sic] Mass book with an English translation. And the same in Pius X hymnal, see attached.

I have a question for the scholars. Listening to the two chants, the Laus Regiae sounds more militant to my ears. It reminds me of a Crusader chant, a time in Church history I would not be keen to evoke.

Why not? As my parish’s pastor pointed out on the Feast of All Souls, the Church on earth is called The Church Militant. Even when we sing the Litany of the Saints, we are calling upon on all the forces of Heaven to intercede for us, The Church Triumphant, to come to our aid. Who needs video games when we’re living the real the thing?! This is what’s wrong in the Church now. We have literal spiritual weapons to help us with the daily fight against the world, the flesh, and the devil. We even have a maledictory blessing and exorcism for ridding places of vermin.

This version has a particularly military feel to it, which is what I like most about it. Unfortunately there’s no sheet music for this arrangement with a drone and some decent harmony towards the end, but it’s my favourite chant version. It has a good pace and doesn’t drag on.

https://www.youtube.com/watch?v=XNreKK--lYk

Is it real, or auto-generated? Sounds unreal, to me. The pace is right, though.

It’s not AI. I don’t know what constitutes “real” anymore in recorded music. It’s likely edited as recorded music is. It’s made by a family who enjoy singing together.

From their YouTube Channel:

We are a family that loves to sing together and record inspiring and uplifting music. Our music is influenced by classical and fantasy literature as well as cinematic, traditional, religious, and classical music. Being a family, we have the unique advantage of similar sounding voices that blend well together. We also have a very broad vocal range potential of over five octaves with a particular focus on singing in the deeper registers. This all enables us to create well blended recordings with a lot of musical depth.