Here it is on A5 paper with an English translation, in the style of the classic version that tomjaw has also referenced; I've eliminated the references to the Queen since those are not generally part of the prayer.

Edited the accent in Cárolus from Carólus. (Edited 2: I am only slowly getting used to using the babel package which includes a slightly modified punctuation for ecclesiastical Latin typesetting; I think it's an improvement on the default.)

Added to GregoBase:
https://gregobase.selapa.net/chant.php?id=18123

Here is a version suggested by our priests.
A change was made on the notes over 'Cárolum'.
To me it sounds better to sing, what do you think?

Added to GregoBase:
https://gregobase.selapa.net/chant.php?id=18124

Here is the previous version from Plainsong for Schools 1940 ed.

One of our choir members has suggested a third option of how to modify the melody to fit the words. We have two problems in changing the melody,
1. The organ accompaniment in Plainsong for schools, may not work with moving the clivis.
2. The congregation will be used to singing the clivis on the first syllable of the monarch's name.

Well we will sing the version I prepared above and see how it goes!

Edit, it all went well today!

@Josh I have been assured that increménta (neuter plural) is correct by several Latinists... But the 'Liturgical' books have increméntum (neuter singular), as you can see from the above scan of Plainsong for schools and the copy of Ritus servandus 1926 ed. a colleague has.

I am unsure if I have the authority to 'correct' those books... I am thinking of producing a second set of resources with the correct Latin and allow people to choose!

As incrementum means growth, ... which is an uncountable noun (mass noun), English would not use the plural, but Latin seems not to take a fixed view, admitting both.

incrēmentum , i, n. incresco,
I.growth, increase, augmentation (class.).
I. Lit., of plants and animals: “quid ego vitium satus, ortus, incrementa commemorem?” Cic. Sen. 15, 52:
...

https://www.perseus.tufts.edu/hopper/morph?l=incrementum&la=la#lexicon

@Chrism: interesting idea; no problem if you take this version as your own best.
Besides, I don't think there is an official version yet...

By the way, instead of:

Cá(fe!d)ro(d)lum :(d.) (:)

you could use one virga + two punctum inclinatum:

Cá(fvED)ro(d)lum :(d.) (:)

______________________
Our choir sung the following version twice already, it sounded alright for us so we are going to keep it: https://gregobase.selapa.net/chant.php?id=18124
It was crafted by two of our priests, talented singers. I endorse their creation.
_________________________
The first accented syllable 'Cá' seems to have focused the attention, thinking more notes should be attributed to it, but another word has the accent on the first syllable: «Dóminum» (accusative case like "Cárolum"). Maybe we could review the whole Graduale repertoire to see how many notes are usually distributed over the three syllables of Dóminus/-e/-um?

Now listen what sounds better when you sing:
« Dó - mi - i - num » (score 18124)
vs.
« Dó - ó - ó - mi - num » (your score)

« Dó - mi - i - num » flows naturally,
« Dó - ó - ó - mi - num » : that doesn't really work, does it? like Mozart would say to Salieri... :-)

Anyway, keep bringing new ideas, always interesting to see what you guys come up with.

« Dó - ó - ó - mi - num »

I think it's rather,

« Do - o - ó - mi - num »

With the accent being expressed only on the last note, like a reverb.

In the past examples we've seen, the accented syllable is always on the re and ictus. I think it sings better that way, but I'd be interested if you heard the congregation sing CArolum or caROlum?

(removed)

Does anyone have an English translation or paraphrase of the "Domine salvum fac" that keeps the number of syllables (aside from name) and (as much as possible) stresses of the Latin text?