What does the Eastern Rite Catholic Church teach on this? I had always assumed that its theology was effectively identical with that of Orthodoxy, with the occassional bow to the "Immaculate Conception". I'm leaving the Maronites out of this for now.
We are identical to the Orthodox on this, although we view the Immaculate Conception as a development of the Orthodox doctrine of Mary as Panaghia (all-holy), therefore always holy. There are numerous ancient texts that refer to the Holy Spirit dwelling in Mary from her mother's womb, and if true it would mean that she was full of grace and illumination from the first moment of her existence.
I think though that many of us are uncomfortable with the 1854 definition placing the Immaculate Conception on the same theological plane as Christology, Triadology or Pneumatology.
We don't worry ourselves with the Latin definition of original sin. Even if the Theotokos was always holy, she still had free-will and could have chosen to turn away from God's plan for her life, just like everyone else.
St. Demetrios of Rostov taught the Immaculate Conception, and the Old Believers were rumored to believe in it. I would prefer to see it as a theological opinion rather than as a dogma, but I will leave that up to the Vatican authorities.