After many failed attempts to build a decent Solo Deck during the Last weeks, i finally build something that seems to work out. So far I won Journey along the Anduin, Foundations of Stone, the Long Dark and Shadow and Flame (never more than 2 tries). Only the Watcher in the Water was a bad experience, the low engagement cost and bad abilities of the tentacles killed me on all 5 attempts.
The Idea is pretty simple, with Light of Valinor and Nenya in play i have plenty of Willpower for the Quest (not even counting on the Ally's). Whit Galadriel and an Unexpected Courage on her, threat was never an issue, and you can use Glorfindel for Questing a few times when you can not find Light of Valinor at the start of the game.
Therefore, you should mulligan for Nenya to be able to play the cards.
Defending can be quite tricky early on and should be the biggest weak point of this deck. Jubayr and some healing to use Glorfindel hit points should help out on this front.
To kill the big enemies, I always wanted to try to get the best use out of Herugrim possible.
Whit Nor am I a Stranger you can play it on Glorfindel and every point of Willpower on him is used 2 times from then on, therefore I use cards like The Favor of the Lady or Strider.
I was able to one shot the Balrog with him having 6 willpower Herugrim and all 3 Copies of Fair and Perilous thanks to Mirror of Galadriel and being able to stay on 0 threat for around 10 turns.
Might not be the fastest way to win, but I had fun anyway.