The association of St. Dominic with the institution of the Rosary is a legend. The meditations on the mysteries were not added to the Rosary for 200 years after his death, while the recitation of the Rosary itself pre-dated his birth. On the 'Hail Mary':
http://www.newadvent.org/cathen/07110b.htm
In point of fact there is little or no trace of the Hail Mary as an accepted devotional formula before about from certain versicles and responsories occurring in the Little Office or Cursus of the Blessed Virgin which just at that time was coming into favour among the monastic orders. Two Anglo-Saxon manuscripts at the British Museum, one of which may be as old as the year 1030, show that the words "Ave Maria" etc. and "benedicta tu in mulieribus et benedictus fructus ventris tui" occurred in almost every part of the Cursus, and though we cannot be sure that these clauses were at first joined together so as to make one prayer, there is conclusive evidence that this had come to pass only a very little later. (See "The Month", Nov., 1901, pp. 486-8.) The great collections of Mary-legends which began to be formed in the early years of the twelfth century (see Mussafia, "Marien-legenden") show us that this salutation of our Lady was fast becoming widely prevalent as a form of private devotion, though it is not quite certain how far it was customary to include the clause "and blessed is the fruit of thy womb".
"The association of St. Dominic with the institution of the Rosary is a legend. The meditations on the mysteries were not added to the Rosary for 200 years after his death, while the recitation of the Rosary itself pre-dated his birth. On the 'Hail Mary'..."
Very interesting.
Based on what you have just said, I am more inclined than ever towards describing the "Hail Mary" as probably being a Western corruption of the Orthodox prayer in the Divine Liturgy, "O Theotokos and Virgin rejoice".