If you change the political landscape (including the political power of your church) there is a good chance that things won't be peaceful regardless of your methods. Humans are full of corruption and there are likely some people who were hungry for power who rose high in the church who don't care for the ideals of the reformation and will oppose anything to hold power - even in a church devoted to Justice.
A few examples from history are given below.
The most successful from the examples below is continual spiritual prompting of your followers, so that they want to follow the 'correct' path rather than the establishment.
Please don't up/downvote based on your opinion of religion/the Bible, this is the best source material I have at hand to answer the question, which is religious in nature.
Flood everyone and start again
The Lord saw how great the wickedness of the human race had become on the earth, and that every inclination of the thoughts of the human heart was only evil all the time. The Lord regretted that he had made human beings on the earth, and his heart was deeply troubled.
The Lord then said to Noah, “Go into the ark, you and your whole family, because I have found you righteous in this generation. Seven days from now I will send rain on the earth for forty days and forty nights, and I will wipe from the face of the earth every living creature I have made.
- Genesis 6:5-6,7:1,4
From your question, this is probably not the non-violent scenario you want to go with as thousands died. Also, it didn't really work and history shows that within a few generations Noah's decedents were almost as bad as the people who were flooded.
Appear to a chosen prophet and perform miracles
Now Moses was tending the flock of Jethro his father-in-law, the priest of Midian, and he led the flock to the far side of the wilderness and came to Horeb, the mountain of God. There the angel of the Lord appeared to him in flames of fire from within a bush. The Lord said, “I have indeed seen the misery of my people in Egypt. I have heard them crying out because of their slave drivers, and I am concerned about their suffering. So I have come down to rescue them.
I know that the king of Egypt will not let you go unless a mighty hand compels him. So I will stretch out my hand and strike the Egyptians with all the wonders that I will perform among them." - Exodus 3:1-2,7,19
Even when people believed that Moses was a prophet, they still didn't follow his instructions. Miracles convinced Pharaoh that Moses' God was real, but he wasn't convinced that Moses' God was more powerful or worth listening to than the Egyptian Gods until all the first born Egyptian boys died in one night. Horrific stuff, with the lesson not to rely on miracles alone to convince people to follow divine instructions.
Write down a list of divine rules and give to the people
When the Lord finished speaking to Moses on Mount Sinai, he gave him the two tablets of the covenant law, the tablets of stone inscribed by the finger of God. Moses turned and went down the mountain with the two tablets of the covenant law in his hands. They were inscribed on both sides, front and back. 16 The tablets were the work of God; the writing was the writing of God, engraved on the tablets. Exodus 31:18, 32:15
Following the giving of the 10 Commandments, God gave Moses and his brother Aaron many more rules and instructions about how to set up the ancient Hebrew church and how the people were to live (see entire book of Leviticus).
However, it didn't work: Having been rescued from slavery in Egypt and given a divinely instituted church, the people complained, immediately did their own thing, and questioned the new authority even in the face of continued divine intervention.
Now the people complained about their hardships. “If only we had meat to eat! We remember the fish we ate in Egypt at no cost—also the cucumbers, melons, leeks, onions and garlic. 6 But now we have lost our appetite; we never see anything but this manna!” Exodus 11:1,4
Miriam and Aaron began to talk against Moses because of his Cushite wife, for he had married a Cushite. “Has the Lord spoken only through Moses?” they asked. “Hasn’t he also spoken through us?” And the Lord heard this. The anger of the Lord burned against them, and he left them. When the cloud lifted from above the tent, Miriam’s skin was leprous. Exodus 12:1-2,9,10
The lesson here: rules don't change people's hearts, so and there'll be friction between the new order and those who liked the old ways better
Civilisation wide hardship requiring dependence on your deity
Following unending idolatry, losing the scrolls of God's holy laws for a few hundred years (to be found accidentally in a pile in the corner of the main temple by the cleaner), and the routine killing of prophets, God tried to beat sense into Israel using Nebuchadnezzar and the Babylonian army.
The Babylonians invaded, and took everyone as slaves back to Babylon. Many who hadn't cared about the God of Israel in the first place integrated with the Babylonian population but were never heard from again. But a core secretly passed notes and became more fervent in their belief and eventually following a few miracles decades later were allowed to return to Israel to rebuild. Israel never had an idolatry problem again, and never lost their holy books again after that - so kind of effective.
In your case, this could work - use an external 'evil' force to conquer your people so that they turn to Justice and actually listen to what he says. Still not death free however due to the conquering and war that precedes the reformation.
A long, slow, grass roots campaign, show how to live by example
A few hundred years after the Babylon thing, Israel had developed religion into the primary political structure. They didn't just obey the laws, but they put new laws in place to make sure people didn't get close to thinking about getting close to breaking the original divine laws. In doing so they became law focussed to the extent that their God send Jesus as a divine incarnation to demonstrate the intent of the laws - not to regulate behavior but to show that people should be loving toward each other.
Then Jesus said to the crowds and to his disciples: “The teachers of the law and the Pharisees sit in Moses’ seat. So you must be careful to do everything they tell you. But do not do what they do, for they do not practice what they preach."
“Woe to you, teachers of the law and Pharisees, you hypocrites! You give a tenth of your spices to the temple—mint, dill and cumin. But you have neglected the more important matters of the law—justice, mercy and faithfulness. Therefore I am sending you prophets and sages and teachers. Some of them you will kill and crucify; others you will flog in your synagogues and pursue from town to town." - Matthew 23:1,23,34
“A new command I give you: Love one another. As I have loved you, so you must love one another. By this everyone will know that you are my disciples, if you love one another.” - John 13:34
This definitely resulted in a reformation - the Christian church was formed out of those Jews and Greeks who believed. But many didn't believe and remained Jewish or pagan. Also, people died because these new Christians didn't follow the old political order and so were a threat to people in power (who succeeded in killing quite a few between then and today).
Continually prompt your people through some spiritual means
The god of Israel came to the conclusion described above that rules don't get the results. You need people to want to be reformed.
This is the word that came to Jeremiah from the Lord in the eighteenth year of Nebuchadnezzar:
"The people of Israel and Judah have done nothing but evil in my sight. But I will surely gather them from all the lands where I banish them in my furious anger and great wrath. They will be my people, and I will be their God. I will give them singleness of heart and action, so that all will then go well for them and for their children after them.
I will put my law in their minds and write it on their hearts. No longer will they teach their neighbor, or say to one another, ‘Know the Lord,’ because they will all know me- Jeremiah 32:1,30, 39, 31:33
This prophesy reportedly came true a few hundred years later after Jesus died when God's holy spirit became available to everyone.
This was probably the most effective form of reformation accomplished that has been documented in the texts, as the result was described with only positive outcomes:
They devoted themselves to the apostles’ teaching and to fellowship,
to the breaking of bread and to prayer. Everyone was filled with awe
at the many wonders and signs performed by the apostles. All the
believers were together and had everything in common. They sold
property and possessions to give to anyone who had need. Every day
they continued to meet together in the temple courts. They broke bread
in their homes and ate together with glad and sincere hearts, praising
God and enjoying the favor of all the people. And the Lord added to
their number daily those who were being saved. - Acts 2:42
While the availability of the holy spirit to anyone who believes was a continual thing after Jesus' death, of course not everyone wanted to be a believer. Deaths from this method are related to those from the previous 'grass roots' method as they both happened around the same time.
Inspire some priests to read and understand the divine texts properly
After the aforementioned reformations, new political power structures developed over a period of several hundred years, culminating in the Roman Catholic church dominating Europe and manipulating monarchs for their own gain. Another reformation was required.
The Lutheran reformation is usually dated as starting 31 October 1517 in Wittenberg, Saxony, when Luther sent his Ninety-Five Theses on the Power and Efficacy of Indulgences to the Archbishop of Mainz. The church had been collecting money to pay for cathedrals in exchange for forgiveness of sins, which Luther said was not how divine forgiveness worked, with reference to the original texts.
The invention of the printing press and literacy enabling the average Joe to read Luther's arguments were vital to the effectiveness of Luther's reformation - before this everyone had to just believe what they were told by their local priest.
Due to the upset of political power Luther caused, this reformation also came with many deaths (see St Bartholomew’s Day massacre painting below).
Summary and discussion
Human hearts seem to be full of corruption, and many people want power even if it means perverting something good. These people will resist your reformation regardless of whether you go in hard or soft.
It might be worthwhile considering the overall aim. Can your deity afford to cut losses, ignore the intransigent and focus on reforming those who are more receptive? If so, can this be done quietly without disturbing the current power balance? Some evil will remain, and likely even be preached, but over time you might be able to inspire many thousands of poorer people to follow the true cause. In time (potentially over several generations), some of these may make it into the halls of power and start to change the whole religion a bit at a time.
It seems unlikely that you'll ever convince everyone (or even a majority?) to follow the new way regardless of method, given free will. So setting up a culture of religious tolerance would help prevent deaths of your true followers at the hands of the others.
Also, the fact that Luther needed to cause a reformation 1500 years after Jesus started the church just goes to show that even the best effort your deity makes now will likely need to be continually followed up as each generation has their own opportunity to turn away from the one true path.