October 7 was the Feast of Our Lady of the Rosary, and October is, traditionally, the month of the Rosary.
The 150 recitations of the Hail Mary was, obviously, connected to the monastic praying of the 150 psalms (especially for those without books or who could not read). The recent addition of another 50 Hail Marys has obscured this connection to the Daily Office, the Prayer of the Church.
There is an old tradition, (presumably older than the division into 15 ‘decades’ – with each ‘decade’ having a ‘mystery’ to reflect on) which simply used the Biblical verses (of the first half of the Hail Mary) concluded with a thought about Jesus:
Hail Mary full of Grace, the Lord is with you. Blessed are you among women and blessed is the fruit of your womb Jesus, conceived of the Holy Spirit during the Annunciation of the Angel.
Hail Mary full of Grace, the Lord is with you. Blessed are you among women and blessed is the fruit of your womb Jesus, who together with you who has conceived him, visits Saint Elizabeth.
There is a full list of 50 endings and more reflections here.
There are ways we might use this approach as an entrance into contemplative prayer. This version may have more ecumenical application. You might produce your own list of endings.