Hi Mike —
The devotion to the Little Office of Our Lady is one that I share as well. Long before I ever recited the Divine Office, I said the Little Office for years. For anyone with deep devotion to Our Lady, it is a very sweet daily prayer, easier to say and far less changeable than the Divine Office, which does require some expertise as well as a current Ordo Missal.
It is, nevertheless, a private devotion and is not a part of the Divine Office, although medieval European clergy often prayed it in addition to the Office, especially on Saturdays. It was also often used by Third Order members and lay brothers as it is easily memorized.
I have attached a link here for a short history of the devotion:
All this being said, if someone is bound to say the Divine Office by promise, then they have to fulfill the duty. Perhaps a conversation with their spiritual director, reflecting on the difficulties in saying the entire Divine Office could resolve this. The Divine Office is the official prayer of the Church, and by participating in it, you join in the prayer of the Bride of Christ, rising up from the whole world.
Generally speaking, the official liturgy of the Church (the Mass, the Divine Office, and the Sacramental rites) always take precedence over any private devotion like the Little Office, the Rosary, novenas, etc.
Hope this helps.