The other rites in the Latin Church were, for all practical purposes, like the Roman Mass itself, done away with and the novus ordo put in it’s place. The Carthusians had their’s till the early 70’s, not wanting to give it up. They now have the novus ordo. While there might have been an offering of the Dominican, Carmelite, Carthusian, Premonstratensian and Cistercian Mass in the times we are speaking of, it was probably rare and not well publicized.
I was able to attend Holy Saturday in Monroe, CT at Our Lady of the Rosary Chapel, where Bishop Robert Mckenna, O.P., says the Dominican rite. Anyone wishing to see how it was should get there one of these days, for he is not getting any younger.
I have heard through the grapevine that there are a few Cistercians in Spencer, Massachusetts who still say their old Mass. This was told to me about 4 years ago.
Wherever you are, ask Our Lord and Our Lady to assist you and guide you to where you can trully, consistently and reverently receive the sacraments of the Catholic Church and be taught and preached the faith without any compromise whatsoever.