After over 25 tries of this scenario with 3 different decks from ringsDB, I am officially concluding that the quest is absolutely impossible to beat one-handed. This was the third (and now final) deck I tried:
http://ringsdb.com/decklist/view/6904/mount-doom-hobbits-1.0
It's a pretty bad deck for this quest. And keep in mind that I played this on "easy" mode where you remove the gold ring cards and start with an extra resource. There's definitely something wrong with this quest if you can't beat it after 25 tries using 3 different decks...on "easy"!
Unless anybody else has a deck that could beat this solo one-handed, I am now forced to try it out two-handed, which I don't have a problem with. I was just hoping to beat it solo, but we now know that the quest is definitely not meant to be beaten using only 1 deck. This makes thematic sense because both Frodo and Sam (2 players....2 decks) were involved with Mount Doom anyway.
Let's hope for the best with 2 decks! I'll be selling off my whole collection (which has everything to date) if this scenario can't be beaten.
Edited by gpd924