There is no Anglican Church.
If you keep that in mind, much of the diaphanous sophistry of the ACI dissipates like a chill mist gradually burned away in the rosy-fingered dawn.
Uses of "Anglican Church" make sense, to be sure, in that they are parasitic on applications of "church" to genuine churches. We know what it means to say "the Church of England" or "the Roman Catholic Church", and the Anglican Communion at times may resemble these, like a glass eye may resemble a live eye--so one might even innocently utter "the Anglican Church" referring to the Anglican Communion.
But Radner and Seitz' uses are rather darker, part of a larger attempt--an effort that I strongly suspect meets with the avid approval of our Archbishop--to impose a reality, an Anglican Church, on the heels of imposing a new usage, where "Church" in "the Anglican Church" is univocal with "Church" in "Roman Catholic Church." So you see, Schofield did not really abandon the communion of this church by joining the Southern Cone--they would seem to say there is no real distinction between the communion of the Episcopal Church and the communion of the Southern Cone because what may seem to some to be their distinct communions are really the same as the one communion of the Anglican Communion.
But that gets the notion of communion backwards--the communion of the Anglican Communion could only supervene on the communions of its member churches, at least for now. That's why, for instance, we say our common life is damaged when some member withdraws from it, as Nigeria's Primate boycotts the Eucharist with the other primates, and threatens to withold its bishops from Lambeth. It can't be that the various communions of the member churches derive their being from the communion of the Anglican Communion, particularly if they exist in such a way that they may withdraw from it and form other, really distinct networks. At most one could argue the being of a member church's communion is filled out or amplified by its being a member of the larger network--a matter not of esse, but of plena or bene esse, a contingency. To get what the ACI wants, the AC would have to change what it is, and its members would have to change what they are as well.
The long term goal seems to at least include the imposition of a centralized, bureaucratic structure, with power of its own to discipline and observe at the level of the Anglican Communion as a whole, an imposition whose practice is carefully circumscribed by a constitution or social contract so as to be incapable of responding to correction from the Holy Spirit that would require communion-wide repentance and amendment of life, as with adoption of the ordaining of women or the breaking down of race barriers. To conservatives, this is merely insurance against what some would call "social justice" and what they might call "liberalism": Amaziah of Bethel banning Amos.
Ironically, the scheme is directly analogous to Gordon Tullock, James Buchanan, and Hayek's thoughts on constitutions and Keynesianism. The idea with Hayek et al. was that economic management by the federal government--as in Social Security, Medicare and Medicaid, WIC, etc--could be eliminated and in the future precluded by constitutional reform, esp. reform locking out deficit spending, and the leading edge of what they saw as socialism. And a general potentially growing threat to the institution of private property could be cut off, or as Norquist would later say, strangled in the bathtub. Buchanan, additionally, saw himself as preserving something precious from the heritage of the Old South. Of course, these guys are all liberals--classical liberals in the mode of Say, Sisimondi, "Smith": what we would now call "right-wing liberals." Structurally, ACI seems to be inthe same boat, so to speak. It is odd--to say the least--to see Williams and Radner plumping for a structural solution to our crises in the style of classical liberalism, of all things.