Was there any interest in emulation similar reforms in other religious traditions? Was there a Russian Luther who never quite made it?
When you say "Eastern Orthodox" everybody thinks of the oriental churches, not of the Russians and the Greeks.
I guess the confusion stems from the Catholic insistance on themselves being the "Orthodox" church as late as in the Catholic Encyclopedia of 1907.
Well, how did the Russians react to the reformation?
Ivan the Terrible really did his best to gain the protestants as allies, or, at the very least, to prevent a similar uprising in Russia. The Stoglavy Synod of 1551 convened to discuss the reformation of the Orthodox church and some of Luther's criticism got implemented. Stoglavy it is called because their decissions were split in 101 chapters (sto-odna glava) on various topics. It included:
A ban on mixed monasteries: Nuns couldn't live in walking distance from the monks.
Monks couldn't be beggars.
Stewards were to be set by each Russian city (their number was only set for Moscow as 7) to control the clergy for "humility, meekness, temperance and lawfulness" (chapters 6 and 43).
The clergy had to set up schools for educating commoners in the scriptures and couldn't deny an instruction to those who requested it. (chapter 26)
"Man-layers" (homosexuals) and "sodomists" (adulterers, johns) were to be banned from the church. (chapter 33)
The clergy was banned from shaving or hiding it's status while sporting lay dress. (chapter 40)
A plenty of limitations were set on how the church could use the land it owned. (chapter 101)
All paintings, and especially figurines, in the churches, except for the icons ("in the Old Greek style or fashioned after such irreproachable icon painters as Andrey Rublev"), were to be destroyed (and Russian emissaries would subsequently barge even into mount Athos in Greece to destroy all the arts there now deemed idolatrous).
In 1570 Ivan the Terrible invited Jan Rokita, a Hussite exile from Bohemia to Poland, to speak on behalf of the Reformation in his court in Moscow. However, Ivan didn't like what he heard and wrote a lengthy point-by-point refutation of Lutheranism (called "Reply to Jan Rokita") denying them even the status as christian heretics. His main rub was their denial of the saints and of a professional clergy, along with an obsession with the Old Testament. So now he declared Luther to be Lucifer and was done with it. In an exchange with Staphan Bathory, Ivan said that "the Latin Religion can be said to be demi-christian, but some of your nobles are Lutherans and that is complete heresy.".
It could be added that Russia introduced divorce and banned forced monastic confinement under tsar Peter the Great, a century earlier than it was done in France and other Catholic nations.
Sources:
Text of the Stoglavy Synod (1551) on wikisource
What about the Oriental Orthodox world of Armenia, Egypt and Ethiopia?