There seem to be cases when the traditional antiphons just don't quote the whole passage, as a sort of "clarification of the meaning so it goes with the readings" thing. Though of course they could be going off a different translation, as you say. Apparently the "Psalterium Romanum" was used in places in the Roman Missal, so maybe that's the source of the difference?

The Clementine Vulgate text is:

"Justitiæ Domini rectæ, lætificantes corda;
præceptum Domini lucidum, illuminans oculos.
Timor Domini sanctus, permanens in sæculum sæculi ;
judicia Domini vera, justificata in semetipsa,
desiderabilia super aurum et lapidem pretiosum multum,
et dulciora super mel et favum.
Etenim servus tuus custodit ea ;
in custodiendis illis retributio multa.

So the bits it's quoting, it's quoting perfectly accurately.

The latter translation is not Nova Vulgata, because it says:

"Iustitiae Domini rectae, laetificantes corda,
praeceptum Domini lucidum, illuminans oculos.
Timor Domini mundus, permanens in saeculum saeculi;
iudicia Domini vera, iusta omnia simul,
desiderabilia super aurum et lapidem pretiosum multum,
et dulciora super mel et favum stillantem.
Etenim servus tuus eruditur in eis;
in custodiendis illis retributio multa."

A commentary on the Psalms by St. Augustine has that "nam" servant thing going, though, so I suspect you're right about it being from the Old Latin/Italic translation.

The "versio Romana" of the Roman Missal is apparently traditionally said to be from St. Jerome's first go-round of translating the Psalms, which he did from Hebrew texts (maybe different texts than ones he got later), the Septuagint (maybe different Septuagint translations than he got later), and the Old Latin and Itala translations (about which we know little, except that the few Latin-speaking Roman Christians were ferociously attached to them and resisted changing them). He knew better than to change certain things too much, because he did that translation when he was still living in Rome.

The thing is, we know his later translations of the Bible (which became the Vulgate) were very Eastern-influenced (and of course, he came from Dalmatia himself) and very post-Jamnian-Jewish-influenced. (And he was out of reach of Roman mobs, living all the way over in Bethlehem.)

The earlier texts of the Septuagint, the pre-Jamnian Hebrew texts, and the Old Latin/Itala translations often seem to have leaned in a different way, interpreted more like what Judaism was like for a Jew in Jesus' day -- before Christianity came along, the Temple was destroyed, and Jamnia encouraged Jews to circle the wagons and distrust anything that came out of the same diaspora they were living in. The Old Latin translations were said to be clumsy, but preserved a lot of this mindset and tradition of interpretation of the OT. (And they were redolent with the amateur, working-class slave, spirit of really early Christianity, as slightly later Early Christians tell us.)

We also have to consider that though the Church encourages Biblical scholarship and going back to the source, she's never said that only the source texts are inspired. So even if an approved Bible translation is abandoned in the end, "what was holy once is holy still". The Biblical commentaries based on the old translation are still valid, and the Roman Missal still used the old translation in bits. So clearly, we are not to regard those bits which were kept as useless and wrong. People went to a lot of trouble in various ages to keep them for us.