After a bunch of playthroughs, I've settled on a version of my "Three Rings" deck that has been able to beat all* scenarios and all nightmare scenarios released to date, with a >33% win rate (usually 100%, but some of the harder quests have encounter and/or player draws that lose). Note that I stopped working on this just before the Grey Havens and the 3rd ring came out
*escape from dol gondur is excluded from this claim. I did manage to beat it once, but I'll need to play through it some more, and see if there is a slight modification that can improve my chances. Regardless, I'd have to play with the rule of "select which hero is the prisoner" rather than have it be random.
Decklist (with notes) - 51 cards.
The deck is 51 cards to allow one card to be removed before each scenario. In some cases, one of the Unique allies might not be usable. In many cases, there are no Condition attachments, so Power of Orthanc isn't needed. In other cases Nenya (Battle/Siege heavy quests), Flame of Anor (location heavy quests), or a Dareon's Runes (against Dunland enemies) might be removable.
This deck can be constructed from 2 core sets, and 1 of each expansion. Note that all unique cards (other than Vilya) are only 1x, just for fun.
Heroes (36 starting threat):
Gandalf
Elrond
Galadriel
Attachments (13):
For Gandalf:
Wizard Pipe
Gandalf's Staff
For Elrond:
3x Vilya
The Light of Valinor
For Galadriel:
Nenya
For Gandalf/Elrond, depending on need:
2x Unexpected Courage
2x Expert Treasure Hunter
A Burning Brand
Ring of Barahir
Events (18):
3x Elrond's Counsel
3x Hidden Cache
3x Daeron's Runes
2x Dwarven Tomb
2x Flame of Anor
A Test of Will
Hasty Stroke
Stand and Fight
Power of Orthanc
Will of the West
Allies (20):
Cheap:
3x Zigil Miner
2x Warden of Healing
2x Vassal of the Windlord
Henamarth Riversong
Arwen
Bilbo Baggins
The Riddermark's Finest
Expensive:
3x Northern Tracker
Faramir
Boromir
Treebeard
Gawahir
Gildor Inglorion
Beoren
If you don't have a second core set, you would have to replace one copy of the following three cards:
Northern Tracker, Unexpected Courage, and Dwarven Tomb
You can also replace the Northern Tracker and Dwarven Tomb with Elfhelm and an Asfaloth. I would make these replacements because Dwarven Tomb normally gets back and Elrond's Counsel for threat control, which Elfhelm can help with, while keeping the same number of 2 atk / 2 def / 3 hp characters. Asfaloth keeps the number of location control cards the same (needed for Journey to Rhosgobel to clear Rhosgobel before stage 2, as well as other location heavy scenarios / encounter draws).
Once the next set comes out, you can use one Shadowfax instead of the Unexpected Courage. Grim Resolve is another possible replacement.