I wonder whether the Crown Nominations Commission should resign en masses, and we should instead choose the next Archbishop of Canterbury in much the same way as the Copts choose their Pope:
Maybe there would be a process of nomination - all General Synod members secretly write down one name, the top twenty go onto the long-list. This would allow the possibility of those not already in the house of bishops to be considered, and General Synod members might be expected to have a sense of what the potential leading candidates are like (!).
Then there would be a vote to produce a short-list. Perhaps all clergy and PCC members in England could have the franchise in this. It ought to be easy enough to organize, rather than a vote of all Anglicans (after all we've no idea who would qualify for that).
Finally an innocent person chooses one name from the three in the bowl (why not have a Muslim do it, just as the keys to the Church of the Resurrection/Holy Sepulchre in Jerusalem are held by a Muslim family, to stop the Christians arguing over it?).
You see, the thing is that this way God can get directly involved (see Acts 1.20-26). And this would give the poor so...chosen candidate a legitimacy which the current system denies. Something which the Church of England could very well use in settling arguments. Something along the lines of "I know there are legitimate disagreements here, but since God has put me here to give a lead, this is how we're going to go forward."
Anyone disagreeing would have to explain why they thought God wasn't careful enough when the choice was made.