Unitatis is, believe it or not, an underappreciated work. It's also, as I detailed in the talk linked above, unapologetically Roman Catholic. Far from giving away the keys to store, UR makes it clear: Christian unity, ultimately, involves reunion with Rome. So it's not "many paths to one center," because ultimately that center is Roman Catholic Christianity. Furthermore, UR distinguishes between dialoging with Orthodoxy, where the conversation takes place among apostolic equals, and ecumenical dialogue with Protestants, where UR admits significant differences still exist.
That being said, in the intervening fifty years--and something I didn't mention last year in Bismarck, developments like the Episcopal-Roman Catholic Ordinariate indicate that progress is being made while still honoring and recognizing the ecclesial traditions of other Christians. We all have roles to play in this journey towards unity, a unity that exists now (in and with Rome) and will exist more fully with God's grace.