I think you are right. We come at the matter from different angles, both of which have their own merits, and our perspectives complement one another.
Personal transformation, if authentic, must lead one to face and address social/political matters, especially with regard to liberation and equality. A prophetic stand against tyranny and a subsequent social revolution minus personal transformation may well lead to another kind of tyranny in the long run.
That being said, I want to move to the next phrase of the prayer: "Your kingdom come. Your will be done on earth as it is in heaven." Jesus refers to the kingdom of God, the core of his message and vision. He calls us to pray that the way of heaven might become the way of earth.
What does the way of heaven (the kingdom of heaven) look like? We know from the other teachings of Jesus, such as those we've been unpacking from the Sermon on the Mount, or the declaration of his ministry as found in Luke 4:18-19. It's the kind of world in which the blind see and the captives are set free, both by the rightful presence and rule of God and through our cooperation. The worship of God and welfare of one another unite to become the primary value around which life is structured.
Jesus' words assume that his followers will want, or learn to want, such a world. The prayer itself may, should,reshape us into such persons. Of course, the more we learn to yearn for God's kingdom to shape the world in which we live, the more open we are to changes in our personal lives and the broader life of society.