I think reconciliation with the church hierarchy is possible, but some kind of face-saving mechanism has to be discovered. Some way that everyone can go away feeling that they have `won.'
For example, what exactly is the heresy that Eadric and company have been accused of? Something about the possibility of demons repenting, I think. Surely someone could word a statement that is acceptable to the church leadership which sounds like it denies this possibility, but leaves a loop-hole open.
Eadric and company could agree to this, and beg re-admittance into the fold of the faithful. The Curia can magnanimously welcome them back, and talk about mercy being mixed with justice, and how they are saddened by the suffering caused by the conflict, and while they were not in the wrong, they would be willing to change certain practices for the sake of the suffering faithful. And they would get to say "the church has always taught that..." so that their precious infallibility would be safeguarded. Inconvenient facts could be ignored by mutual consent. Symbolic gestures of penance and reconciliation could be engaged in by all sides, and things could settle down a bit.
Hethio could retire and work off his taint in some hermitage or monastery. Brey could take over the Temple Guard. Tramst could lead the inquisition- he would be acceptable to both sides, I think. Heck, Tramst might even be acceptable as prelate of Morne!
It would not exactly be peace, but it would be a lot less bloody than the alternative.