Apparently there is a new impetus in creating denominations to suit. This is a very good idea. Now I have a number of imaginary friends who sit on my shoulders and whisper into my ears, and so a number of us are going to start some new denominations. We can't quite agree, so we are cutting the salami quite thinly:
Unitarian Anglican Church
This is an Anglican Church in all its usual features except that the liturgy is rewritten to replace the doxologies and other areas that refer to the Trinity, rather like the Free Christian side of the Unitarians did with their liturgies in the nineteenth century and finally, seriously, in 1932. It would adapt creeds and articles accordingly (the central European Unitarian tradition has a catechism and, indeed, bishops). The Eucharist would be celebrated but selected lay people could preside. The Gospel and other readings would continue with the lexionary but other readings would come in.
Anglican Unitarian Church
However, this is more like the Unitarian Church of today, a Church that evolves its beliefs and sympathies, and in the United States has distinctive liberal Christian, religious humanist, Eastern and Pagan constituencies, but adopts again a more liturgical approach to worship. It would not use creeds and articles as such, or if it did they would be understood as non-confessional historical documents and not exclusive. If there were bishops they would only be superintendents that dressed up. If the Eucharist is celebrated it could be lay or minister led. Whilst the Bible is usually read, according to choice, other sources exist for the other readings.
Liberal Anglican Church
This would continue as an Anglican Church, but follow the marginalising of the historic formularies and do the same across all confessional statements and scrap the promises for clergy regarding belief. People would take theology as it exists and simplify it for preaching purposes. You would expect a wide expression of Christian belief in pulpits from Open Evangelicalism through to non-realism, and from Radical Orthodoxy to nihilistic textualism. The maintained Eucharist, perhaps opening out to some lay presiding, would have a whole variety of interpretations. The Bible lexionary would continue including the Gospel (without obvious intepretation and limited expectation regarding any guidance).
Anglican Liberal Church
This might be Liberal Catholic and Liberal Protestant (as in Europe) in emphases, and will have strayed into multifaith expressions and a variety of theologies. It would have Anglican features: in its forms of liturgy that included but went much further than Anglican inheritances (incorporating elements of other faiths), and variable understandings of Catholic and Reformed ministry, without having to give credal promises. The Eucharist would be one of several dramatic rituals and could be led by anyone. There would be a variety of scriptural and other sources for services, but there may be a pattern to Biblical readings introduced.
Free Anglican Church
This is an Anglican Church that has done nothing but marginalised all its credal and other statements; the name suggests it goes more towards the Reformed side than the Catholic, but would do so only like the Methodist movement did, and so some would be high. It would also reduce the powers of bishops over priests, and in fact might so organise itself that each were rather like the other in responsibilities. The Eucharist could be lay or minister led. The Bible would have set readings but other material also read in services.
Anglican Free Church
This would be a Protestant Church that becomes more Anglican in features, perhaps a series of independent Churches that gather together. It might develop bishops from below, along with councils and other meetings. It would have quite a span of belief, but not as wide as some. The Eucharist could be lay or minister led. There would be some greater emphasis on using the Bible as a guide to God and life.
All these Churches would be socially inclusive, so there would be no bar to ministry on any bases of gender or sexual orientation. Indeed selection for ministry would be task and education based, that is meeting competencies of pastoral support and management, as well as knowledge of and sympathy for the ethos of the Church.
For me, any of these would be better than the current Anglican Church of England (and, if you can average it, the Communion), but the best would probably be the Anglican Liberal Church and then the Anglican Unitarian Church.