For purposes of fitting into one essay an ambitious and comprehensive evaluation of this idea, it will be presented as a statement of theses with only modest support at the present time for each. This may fuel discussion, and certainly will be followed by more attention to many details. That is, this may turn out to be Part I.
To begin with, the Anglican Communion has dropped the ball, and so its various churches cannot be considered the heirs of Anglican belief. Rather, the heirs are the Continuing Church bodies who have accepted The Affirmation of St. Louis. The relatively small membership of Continuing Anglicans, against the millions who belong to the Anglican Communion, the Roman Catholic Church, the Orthodox Church and the various Protestant churches, is not relevant to discussion of beliefs and of the Anglican approach to Right Reason. For this discussion only ideas matter, coupled with facts about history and the current state of the Universal Church.
Those who believe in Demonology, as a true subsection of theological science, should consider the theory that Anglicanism has been attacked by the forces of Darkness precisely because of the potential it had to reunite the Universal Church. Not only does it have the necessary Reason to reunite the Church, but to empower it with a practical approach to theology that would arm the Church to encounter its mission more strategically and effectively than anything the modern world has seen.
The "Liberals" in the modern Anglican Communion have perverted the idea of "the Bridge Church" to indicate a soft approach to ecumenism that amounts to nothing but attempts to compromise, to run from meaning to vagueness, from definition to confusion and from principle to laxity. But, the true principles that could yet, if allowed to prosper, build the bridge that has potential to reunite the Universal Church, would have to be strong enough to endure every assault, unlike the false start that brought the Cantuarian project to moral and doctrinal collapse in the closing decades of the twentieth century, with the collapse still rumbling.
...and members in particular
Every apostasy must be, first and foremost, rebellion against the house in which that apostasy arises. Apostate Anglicans had to reject the specific form of Christianity known as Anglicanism and Episcopalianism. They had to destroy its doctrines and sacraments, and they had to replace the Book of Common Prayer with something enough like it to fool a large number of people. Therefore, it is not correct to see the apostate condition of modern Anglican churches in the Canterbury communion as some natural or inevitable result of Anglican beliefs; for those beliefs first had to be buried and forgotten.
People who live on the two poles of Anglican partisanship, employing the words "Protestant" (or "Evangelical") and "Catholic" by in-house definitions unique to Anglicanism, need to work at finding the reconciliation of their divergent positions that is, in fact, within the actual properties and contents of Anglicanism. This includes the development of Anglican theological thought and liturgical practice over centuries in which responsible churchmen found solutions to relevant issues facing their own respective generations. For example, the writers of the Thirty-Nine Articles addressed the needs of their time with language easily misunderstood today: But, what they actually taught, upon genuine and honest study, was as essential to the Catholic Faith of the Church as the later emphasis of the Oxford Movement proved to be in its time. The two do not contradict each other, but rather complement each other across the centuries.
Divergent practice, and to a degree divergent theological views, can and must be reconciled by what we have in our own possession. This requires, also, that each avoid extreme views that exclude orthodox believers of the other party, that we overcome the ignorance that enables prejudice and misunderstanding on our own part, and that we hear each other with willingness to learn instead of eagerness to react. The result will be, for many, rediscovery of the true Catholic and Apostolic Faith that each of the two parties on each pole have only in part, unless and until they reconcile spiritually and intellectually with the other. Neither party, the Evangelical party nor the Anglo-Catholic party, when refusing to hear the other, have the complete picture; though sadly, the partisan elements among them often exhibit a sense of self-sufficiency and wholeness that is, in fact, an illusion. Evangelicals who think they have no need of Anglo-Catholic respect for the Universal Church and the Sacraments, and Anglo-Catholics who think they have no need of Evangelical emphasis on Scripture and salvation, are both condemning themselves to severe spiritual deprivation.
Myths of consensus
Because the older division of the Church was between the East and the West, we have tried to be faithful to a consensus of the Universal Church that was expressed in the Seven Oecumenical (or Ecumenical) Councils. The Affirmation of St. Louis affirms all seven of them. Opposed to that correct definition of "consensus," it is factually wrong to mistake an ancient consensus of East and West for a modern consensus of Rome and Orthodoxy. In fact, the continued division between Rome and Orthodoxy is deeper than the division between Rome and most forms of Protestantism in the West.
The notion that the Orthodox Church sees the Roman Magisterium as closer to themselves then, for example, the Southern Baptist Convention, is debatable. The two western bodies, from the Eastern Orthodox perspective, share beliefs that rely on Augustinian and Anselmian paradigms 2, and are therefore closer to each other than to the Orthodox Church. In some places, including Holy Mount Athos, the rejection of Roman Catholicism is more fierce than anything to be found in most of the Protestant churches, even the most anti-Roman of them. Just how much we may speak of East West consensus as any sort of Orthodox and Roman consensus, is highly debatable. The former is a historical reality that alludes to the Seven Oecumenical Councils, the latter a deception that alludes somewhat to a grand fiction.
Some writers confuse later Roman Catholic developments with Universal Consensus. A perfect example of this confusion was caused by the fallacy that Rome's dogma of a punitive Purgatory with temporal punishments, including the Medieval and modern "Treasury" doctrine unique to Rome, was ever a doctrine of the Universal Church. Such late developments have no claim to Universal Consensus, and as doctrine are rightly rejected by Anglicans, by the Orthodox Church and by the many Protestant bodies.
...to get back homeward
If we were to look for a Church that has found a sure path back to Antiquity, and also has worked its way back forward with all of the essential doctrines and practices of the One, Holy, Catholic and Apostolic Church, we would need look no further than our own native ground as Continuing Anglicans. We find that full Catholic doctrine in our Evangelicalism, and in our Catholicism; we practice it in our liturgy and experience it charismatically in the sacraments, including the five sacraments of the Old Testament that were spiritually and significantly enhanced in the Church as revealed in the New Testament (one partly corrupted from anointing for healing to "extreme unction" and one a state of life called matrimony). We experience it also in the other two sacraments that are generally necessary to salvation, which we call sacraments of the Gospel, instituted by Christ with a visible sign and ceremony ordained of God, namely Baptism and the Lord's Supper.
Indeed, by explaining the correct meaning of Article XXV, as I have just done in the paragraph immediately above, I mean to show the way home, the path back to Right Reason.
1. Chesterton, G.K, What's Wrong With The World, 1910 1910, London, chapter 5.
2. My brother, David Bentley Hart, however, made the argument that St. Anselm, properly understood, can be reconciled to Eastern Orthodoxy, especially by comparing his work to that of St. Gregory of Nyssa. - Hart, David Bentley, The Beauty of the Infinite, 2003, Wm. B. Eerdmans Publishing co., Grand Rapids.