Great question. I suppose that she wont do anything publicly. Britain is on the verge of constitutional crisis along two axes. Your suggestion would strain both. The Brits love their royals as long as they stay on the celebrity page and off the news. Meanwhile the pressures are mounting for disestablishment of the CofE. Already the new Prime Minister wants nothing to do with bishop appointments. With the state pulling away from the church, it will not be long before the church is extricated from the state as well. So the Queen meddling in church matters is no solution.
Also, the word on the street is that she is not pressing for traditional Christianity but the preservation of the Communion. This is no help as the ABC is increasingly being pressured to choose sides. If he chooses sides, the communion will split. Remaining on the fence will not be an option for long.
With the state pulling away from the church, it will not be long before the church is extricated from the state as well.
Would this be a bad thing?