Caesaropapism in Orthodoxy makes this unlikely. As long as the state has as much control of the Church as it does in Orthodoxy, an incensed people can always turn to the government to remove and replace corrupt officials. In a way, the amount of power Lutheran princes gained over the churches in their domains after Augsburg made those churches a lot more like Orthodoxy. On top of this, the fact that Orthodoxy isn't as centralized as Catholicism means that problems or corruption in one autocephalous (meaning it has its own patriarch/head and isn't answerable to anything short of an Ecumenical Council) Church won't be seen as indicative of the whole structure being corrupt, and prelates from other Churches can take the corrupt Churches to tax by excommunicating their members, appealing to Constantinople, etc. The people can always say "Well things are going fine over there, it's just the priests over here that are corrupt."
Furthermore, the intellectual history that inspired the Reformers just doesn't exist in the East. As I've said every time someone posts a thread like this, what ultimately allowed the Reformers' to form their doctrines about how their churches should be governed and what constitutes right Christian belief was the rediscovery in the West of ancient texts like the Greek New Testament, the Non-neoplatonic Plato, Aristotle, etc., since this spurred the desire to return "ad fontes" or to the original sources. It was through this process that some Western Christians came to the conclusion that there were inconsistencies between what Catholicism teaches and what Scripture says. But the texts that enabled this to happen had always been extant in the East and had a long history of use which shaped how they were viewed there. Further, there are certain arguments the Protestants made which wouldn't make much sense to Easterners, given that they operate in a completely different theological milieu (the iconoclasm of the Reformers will be a non-starter for sure, given how much Orthodoxy venerates the Seventh Ecumenical Council and how well-known St. John Damascene is among Eastern theologians).
So in short, this is a scenario that will be hard to pull off, and more likely than not would have to be a top-down reform in a country where the state has a lot of power. The best I can do for you is have a Tsar impose something like Protestantism out of Europhilia, but this will be rejected by the populace as being too Western and will be very hard to enforce. It would help tremendously if the changes are indigenous. Maybe an early Rasputin-like figure is the way to go. It's very hard to enforce doctrinal conformity in Siberia, and so perhaps a "mad monk" who spent a lot of time there forming Protestantish doctrines and ideas of how the Church should be run eventually worms his way into the Imperial Court, causing the Tsar to impose his beliefs on the people, although he probably won't be completely successful and will have to use a lot of violence to get it done.