“For most of its 2000-year history the papacy has not been in the forefront of reform. It has supported reformers and it has taken over and controlled reform once it has begun, but only once, in the late eleventh century, can it be said that the popes found themselves in the invigorating but dangerously exposed position of being the leaders of a radical party in the church.” (Jonathan Riley-Smith, The Crusades: A Short History, p 4)
The crusades, yes, were part of a reform movement. The Holy War in the East was as much a part of this reformation as the Peace of God in the West. Both sought, in part, to correct the chaos and violence tearing apart Christendom, in different ways.