It's not the Curia who is trying to frame Eadric- it is the bishop of Hethio.
Look back at the membership of the Curia:
the Bishops of Gibilrazen, Hethio, Jiuhu, Kaurban, Mord, Thahan, Tomur and Tyndur; the Inquisitor General and the Grand Master of the Temple Knights; and “One Devout Layman” – a member of the laity selected for demonstrating particular holiness and faith. The last position is currently held by the Marquis of Iald.
Melion, the Inquisitor General, is dead, and Tahl, arguably his legitimate successor, is the one who broke Eadric out of jail. The Grand Master of the Temple Knights, Lord Rede of Dramore, is also dead. He died just before resigning due to reasons of conscience.
Gibilrazen, Hethio, Mord, Thahan and Tomur voted for Eadric's impeachment. Hethio, of course, is a liar and a murderer. I don't think we've heard at all of the other four bishops who voted against Eadric.
Kaurban and Jiuhu voted against the impeachment. I don't think they really have any problem with Eadric. The Marquis of Iald, who also voted against it, certainly doesn't- he later seceded from the Church in protest against the corruption of the Church leadership.
The bishop of Tyndur abstained, but is now a supporter of Eadric, voting against any and all Curia decisions.
So the Curia is diminished and divided. The bishop of Hethio is taking the initiative, certainly, but I doubt any of his fellow bishops would stomach his tactics.
And what happens when someone investigates Lord Rede's death with the appropriate divinations? They found the identity of the Prelate's assassin pretty easily. Who do you think the Temple Knights will support when they learned who killed Lord Rede, and why?
No, bishop Hethio is going down. And when he does, opposition to Eadric from within the Curia will collapse.