What's an "Encounter Deck"?
Some Sort 1653
This is a four-deck fellowship built around a simple idea: the three biggest tools the game has to defeat you are revealing cards, combat, and threat. So let's completely eliminate the danger of all three.
Doom Hangs Still prevents the deck from ever revealing cards. Provided you have the resources to pay for it, Tome of Atanatar and Erebor Hammersmith let you play it up to 15 times in each journey through your deck. Three copies of Will of the West lets you recycle it up to 60 times. That's 60 rounds with the encounter deck revealing no cards.
What about cards revealed during setup? Advance Warning prevents enemies from ever leaving the staging area, and since you're not questing, most enemies can't do anything to you from there. As with Doom Hangs Still, Advance Warning can easily be recurred up to 60 times, if that's your cup of tea.
With one deck devoted to recurring Doom Hangs Still and the other to recurring Advance Warning, that leaves two more decks in our fellowship that set them up and eradicate threat. For this, we have the Song of Eärendil / Wandering Took combo. This lets you pass threat freely around the table from one player to another. Elrond's Counsel is vital for absorbing all the first-turn doomed cards, but late-game you might prefer some massive one-shot threat reduction. The Fall of Gil-Galad is limited to one per deck, but it's not unique; slap four of them on Treebeard and have him sacrifice himself for 49 points of burst threat reduction. Or let a bunch of enemies into the staging area, use Advance Warning to keep them there, and let Damrod eliminate double-digit threat at a time.
Heck, even Sneak Attack Gandalf is good for 5 points of threat reduction, and with three copies and potentially three straight plays, that's 30 points per deck over the course of the game. (If you don't need the threat reduction, Gandalf is also a great choice for taking out enemies in the staging area that you're refusing to engage; if, for instance, they come packing Archery). And who can forget the Aragorn / Desperate Alliance combo; with this particular hero lineup, he can eliminate 92 points of threat per game.
The trickiest part is the first planning phase. These four decks are designed to be played in the order they are listed. Player 4 needs to get down a turn 1 Legacy of Númenor, and then everyone else should play as many Deep Knowledges as they can without threating anyone out, using Elrond's Counsel to get more plays. The first player absolutely must get out one Wandering Took and one Song of Eärendil on Glorfindel or Merry; this enables him to take threat from another player at will, which is important since he has the lowest starting threat. If possible, get a Song of Travel on one of Player 3's heroes so he can play his own Elrond's Counsels.
Player 2's job is getting more Song of Earandils on the board. Eventually, you want one song on each player. Also, if the first player completely whiffed on getting a Took out, Arwen + Legacy of Numenor = 3 spirit resources, which is just enough to get the Took / Song combo started. Otherwise, start working on getting Song of Mocking on Glóin; eventually, with all three on Glóin, he'll be able to draw 15 damage a round from Treebeard, which works out to 15 extra resources.
Player three needs to save two resources for advance warning, but should otherwise work on getting some healing on the board to start the Glóin resource generation engine. And player 4 needs to get a Doom Hangs Still down in round 1 or else all was for naught; Gloin's 1 resource + Legacy of Numenor + We Are Not Idle + Hope Rekindled will do the trick.
For additional resource generation, Love of Tales should wind up on every hero at some point; over the life of the game it'll easily add 8-12 extra resources per copy, since there are a ton of songs in these decks. Resourceful might seem like an odd choice given the amount of doom, but remember that the decks can move threat at will; if all four decks have 40 threat, you can give 7 extra threat to three of the decks, taking them to 47 and dropping the fourth deck into secrecy range. This way each deck can play all of its secrecy and all of its valour cards in the same planning phase.
Once you get through the first couple rounds, things get pretty stupid. You'll be getting a half-dozen resources per turn per deck and will have pretty much as long as you want to do what you want. I've included some options for further shenaniganery- you can Out of the Wild and The Door is Closed! away most of the encounter deck before turning on the quest phase again, or you can use three Gildor's Counsels every round so the encounter deck only reveals one card. You can stack 100 resource tokens on Gloin and then drop a Lay of Nimrodel to let him powerquest through an entire stage at once.
If you wanted, you could even sub in Legolas and Blades of Gondolin to defeat the quest without ever going through a quest stage. Or recycle Ravens of the Mountain to do the same thing. Really, once the encounter deck is no longer revealing cards, and once enemies are no longer engaging once they're revealed anyway, there are a lot of options for what to do. The underlying card draw / resource generation / Doom Hangs Still / Advance Warning engine is so powerful that you can chrome it out however you like and it'll still work just fine.
This is all just a basic engine, and is by no means fully optimized. You can reshuffle stuff around as needed. The basic idea is just lots of Doom Hangs Still, a ton of card draw to ensure that you get to it early, some sort of resource acceleration to ensure you can pay for it, and then threat reduction and some way to deal with enemies that got revealed during setup. It's capable of completely trivializing any quest in the game with a massive degree of consistency.
Just don't expect it to be very fun to play. :)