In defense of the ACC, I again say I am only new member of it (only since 2001), and am learning slowly bit by bit the history of the Christian church in the British Isles, but since I have joined this particular church, which our Bishops and our Archbishop stress is a continuation, rather than an innovation, I have yet to hear anyone teaching me about the history tell me that the ACC supports any other doctrine than Transubstantiation. Indeed, we have in the past, lost the interest of several Episcopalians who quibbled that CONsubstantiation was the proper form of worship. Apparently, we were too Catholic for them in that respect.
I must also add that our church is NOT NOT NOT under the auspices of the Archbishop of Canterbury, just as it is not under Rome. This distinction was made clear by the fact that the ACC was formed to decisively distance the Anglican Communion from the heresies that were acted upon in the 70s...hence the Affirmation of St. Louis. Please check out the site if you wish to know more about that. The links are on the left hand side of the main page.
We use the BCP because it is closest to the traditional liturgy that the ACC wishes to uphold.
Most here, I would hope, would understand that the Continuing churches are, by and large, not in communion with the Archbishop of Canterbury. (Nor, in general, with each other, though there is movement in that direction.) As being under the auspices of the AoC, technically only the Church of England is.)