This is the deck I used to beat Shadow and Flame solo, progression-style. It must be powerful, since it did the deed first try. The deck seeks to vomit allies at a surreal rate to feed and overwhelm Durin's Bane.
Don't be deterred by the high card-count, because Daeron's Runes and We are not Idle are here for the sole purpose of thinning the deck down to (virtually) fifty. In your opening hand, look for anything to help you play allies faster (which is pretty much anything in this deck).
In the early game, just focus on questing successfully, maintaining the status quo by clearing enemies and locations, and playing allies to defend the Balrog's attacks. Once you hit critical mass, you can start hitting the Balrog like a truck with your Battlemasters and nothing should stand in your way.
This deck techs fairly well against this quest. For example, all the effects that boost the Balrog's attack are useless. However, some cards can really wreck your day and must be handled with care. Second Hall is pretty much an insta-loss, and Counter-spell also proved problematic during testing. Either way, you shouldn't have too much trouble beating Shadow and Flame with this deck.
Thanks for reading!