Byzantine Origins?

Many of the longer non-scriptural antiphons and such of the Roman Rite, such as those appointed for Lauds and Vespers of the Octave Day of Christmas (used in the Little Office for Christmastide till the Presentation), are in fact translations from Greek troparia.

I wonder if Greek origins lie behind certain of the well-known Marian versicles (also used in the Little Office), such as Dignare me laudare te, Virgo sacrata - Da mihi virtutem contra hostes tuos, or Post partum, Virgo, inviolata permansisti - Dei Genetrix, intercede pro nobis, and Gaude, Maria Virgo - Cunctas hæreses sola interemisti in universo mundo: for the latter two seem to stem from parts of one of the Roman Matins responsories for the Annunciation, and this text itself seems to betray a Greek liturgical origin by its very floridity, although its roughly rhyming lines may instead shew it a native Latin composition (I give its verse in its older form, as preserved in the Dominican Breviary; the Roman now quotes St Luke i, 45 - Beata es quæ credidisti: quia perfecta sunt ea, quæ dicta sunt tibi a Domino):

R/. Gaude, Maria Virgo, cunctas hæreses sola interemisti,

quæ Gabrielis Archangeli dictis credidisti:

* Dum Virgo Deum et hominem genuisti,

et post partum, Virgo, inviolata permansisti.

V/. Gabrielem Archangelum scimus divinitus te esse affatum:

uterum tuum de Spiritu Sancto credimus imprægnatum:

erubescat Judæus infelix, qui dicit Christum ex Joseph semine esse natum.

* Dum Virgo Deum et hominem genuisti,

et post partum, Virgo, inviolata permansisti.

Gloria Patri, et Filio, et Spiritui Sancto.

* Dum Virgo Deum et hominem genuisti,

et post partum, Virgo, inviolata permansisti.

(R/. Rejoice, Mary Virgin, all heresies alone thou hast crushed, who believed the things Gabriel Archangel said, * When, a Virgin, thou brought forth God and Man, and after birth, inviolate thou remained a Virgin. V/. We know Gabriel Archangel to have spoken by divine agency to thee: we believe thy womb was impregnated by the Holy Ghost: may that unhappy Jew blush, who said that Christ was born of the seed of Joseph. * When, a Virgin, thou brought forth God and Man, and after birth, inviolate thou remained a Virgin. Glory be to the Father, and to the Son, and to the Holy Ghost. * When, a Virgin, thou brought forth God and Man, and after birth, inviolate thou remained a Virgin. )