I'm not sure what you mean by Jung's turn to mysticism later in life. As far as I can see, he tried to maintain his empirical, psychological approach in his writings until the end. Others from a more 'scientific' background might have perceived such writings as mystical, given that they made much reference to alchemy.

In his private life, you could say that his 'mysticism' started in midlife, i.e. in 1913 at the beginning of his 'confrontation with the unconscious'. His account of this, now known as the Red Book, was not made public until 2009. He also kept, or at least attempted to keep, his Seven Sermons to the Dead private.

With regard to a new Reformation for Christianity, we'll have to wait and see. Jung's approach is as good a starting place as any.