A great question!
Although I was never a Latin Catholic, I came from a heavily Latinized background and only slowly moved spiritually toward a more Eastern Christian perspective.
So what can we make of the Fatima devotions from this perspective then?
I found there was no need to give up the rosary at all. Acquaintances of mine who were “echt-Eastern”

were very much against the rosary.
However, I found that the same devotion i.e. 150 Hail Mary’s divided into decades has been around in Orthodoxy, especially Russian Orthodoxy, for many, many years. The great Russian saint (also recognized by Rome) St Seraphim of Sarov prayed the rosary/rule of the Mother of God daily and expected his spiritual children to pray it daily as well ("Staretz Zechariah: An Early Soviet Saint"chapter six).
He even taught that the rosary/psalter of our Lady was revealed to a monk of the Egyptian Thebaid in the eighth century and that all Christians once said it etc.
St Seraphim also said that, in a vision of the Mother of God, he was told by her that the rosary is THE most important prayer to obtain her intercession and protection over our lives - ahead of any other kind of Marian prayer.
The Old Believers of Russia have always had a “Theotokos Lestovka” with 150 small notches divided into decades by larger ones. I have one of these myself and the Old Believers teach that anyone who has prayed the rosary/rule with Hail Mary’s daily will be accompanied by the Most Holy Mother of God after death to each of the toll-houses our souls will visit . . .
So, from an unashamedly Eastern chauvinist point of view, our Lady at Fatima was simply reminding Western Catholics about her beloved Eastern rosary prayer . . .
As for the scapular - this represents, first and foremost, the Holy Protection of the Mother of God which is a great devotion in the East (i.e. when the Mother of God extended her mantle of protection over people in various crises).
The West also has pictures of Our Lady of the Mantle (aka a form of Our Lady of Mercy).
But nothing like what the East has . . .
Interestingly enough, there is an actual Orthodox icon of Our Lady of Mount Carmel in an Orthodox Ukrainian monastery in the town of Horodyshenske called the Mother of God of the Scapular (sic) and listed in Prof. Poselianin’s monumental work “Bogomater” or “the Mother of God” where he lists hundreds of miraculous and locally-venerated Orthodox icons and festivals.
The problem with Fatima from the Eastern point of view is not with its devotions, but with how Fatima was and is used by certain Catholic groups to convert/proselytise Orthodox. The phrase 'Russia will be converted" has been taken to mean by these “Fatimist” groups as meaning “converted to Roman Catholicism.”
I know an Orthodox priest who accepts Fatima and says that her prophecies have been fulfilled in Russia since the churches there are full and the Mother of God is highly, highly venerated (more than in the West).
Alex