The Fellowship contract is a place-holder for the The Grey Wanderer contract. When playing The Grey Wanderer contract, search your deck for Golden Shield. That instantly makes Eowyn a 5 Hero to defend on turn 1, if needed. Mulligan for Herugrim, Unexpected Courage, and/or Steed of the Mark. Once Herugrim, Unexpected Courage and Steed of the Mark are in play, Eowyn will be an awesome 4 (5 with her ability), 5 and 5 Hero that can quest, defend, and attack.
Want to make Eowyn even more awesome? Miruvor, Astonishing Speed, Courage Awakened, and Lay of Nimrodel will all increase her for a phase. Played during the Quest phase, she could possibly quest with 10+ . Played during the Combat phase, she could possibly become a 10+ and 10+ Superwoman. Take that, Eowyn.
If you need a quick way to gain resources to play Herugrim, the contract can be exhausted during the Action window of the Planning phase to gain 2 resources, although that might waste the other selections (especially during the early game). Otherwise, wait to use the contract until the Quest or Combat phase.
I am assuming Heed the Dream, the only other off-sphere card, can be played via the contract during the Action window of the Planning phase, so long as no non-unique Ally or Attachment cards were played during that same Planning phase. But in-sphere unique Ally or Attachment cards can be played without affecting the "first non-unique" status. So I am assuming I can play Herugrim, Éomund, Gamling, or Háma and then Heed the Dream, but I can't play Escort from Edoras, Westfold Horse-Breaker, Westfold Horse-breeder, Miruvor, Resourceful, Steed of the Mark, or Unexpected Courage before playing Heed the Dream.
Other notes: I am posting this deck to hopefully get some suggestions, but I did realize that I am using 16 cards that all revolve around readying, so that may become overkill. I will look at ways to reduce and shore up other possible weaknesses, especially since the contract gives a readying action ability as well.