I just got done running the second scenario with a leadership/lore deck using the spoiled version of Bilbo Baggins.
If you haven't seen it yet, he allows the first player to draw an additional card. Playing solo means you get to draw 2 every turn, and helps make an already fast deck like leadership even faster. Because I was using Theodred (After Theodred commits to a quest, add on resource to another hero's pool) I was able to give Bilbo 2 resource a turn. By playing Son of Arnor I was able to enage the Hill Troll during the Planning phase, which together with the extra resource allowed me to put a Forest Snare on the Troll in round 2 before he was able to attack me.
Drawing the extra cards let me quickly get to Steward of Gondor (then I was at 6 resources a turn) and Celebrian's Stone (giving Bilbo +2 willpower). I was able to Sneak Attack with Gandalf 2 twice. Because Bilbo was getting 2 resource a turn, I was able to get out 2 Daughter of the Nimrodels. My final score was 27.
By using this combo you area able to draw the same number of cards and generate the same amount of resources as 2 players, Once The Hunt for Gollum is released, I think will be a very powerful deck for solo play.