I present here a pair of decks (the lists are at the end of the post) that have a high success rate against most quests. The idea behind them is to exploit Boromir as much as possible. The Song deck attempts to play as many cards as possible as quickly as possible. Often, though not always, it will draw the whole deck on the first turn. With 3x Love of Tales, it then plays down all its songs (making sure to put a spirit, lore, and leadership song on Boromir) and collects a large number of resources. Then it uses parting gifts to pile a bunch or the resources on Boromir, and also plays Dunedain Cache, Dunedain Signal, Burning Brand, Gondorian Fire, Blood of Numenor, and Burning Brand on Boromir. This essentially turns Boromir into a hero with 10+ atk, 10+ def, sentinel, ranged, immune to shadows, with unlimited readying power.
The Boromir deck is full of cards to get some bonus resources on Boromir, Like Steward, Resourceful, Gaining Strength, etc, as well as 3x Gondorian Fire and 3x Blood of Numenor. And of course it has tons of threat reduction.
For Siege and Battle Boromir can regularly quest for 40+ with this setup. For Normal questing, the Song deck has 3x Lay of Nimrodel which can be played on Boromir. Often 2 will be enough to quest through a stage, so with Will of the West this can be done 3 times. For quests with more stages than this, a second or third Will of the West is recommended.
As a test of the decks' strength I used them against The Battle of the Five Armies Nightmare. This is a brutally hard quest in Nightmare, but I think it is a good benchmark for decks because it requires good questing, attack, and defence, and severely punishes decks that take a while to set up.
As an extra test of the decks strength, I actually play the quest as if there were 4 players in the game (i.e. I flip 4 cards every staging, count X as 4, etc.).
P.S. I've only started working with this concept and I think there is room for a lot of improvement. For example, the Boromir deck could have Bifur and 3x Desperate alliance - then it could pass Bifur to the lore player at the beginning of the game and pass it another resource, making the Song deck setup extremely reliable. For quests where the Song deck doesn't have to hold on to certain cards like Lay of Nimrodel for more than 1 turn, you could swap in the upcoming Erestor hero.