After many deckbuilding attempts which ultimately failed against Into Ithilien, I finally had to play a Vilya deck to beat it. The main problem before this was not being able to keep up with the encounter deck, even with as much readying as I could get...
Elrond is included to make use of Vilya, Aragorn to lower your threat before stage 4 so it doesn't gain Seige, and Glorfindel because who else do you choose to keep starting threat low (plus he's great at traditional and battle questing). Together, The House of Elrond makes a formidable team.
You are looking for Vilya or at least a Master of the Forge in your opening hand. Vassal of the Windlord is another card I'm happy to see in my opening hand. Imladris Stargazer is great for getting the most out of Vilya, but the deck is built to be OK without her since there are only 2 events and a bunch of allies. All the attachments are traps to snare enemies, or readying effects. Unexpected Courage usually goes on Elrond so you can use Vilya and his stats.
There are plenty of out of Sphere allies that you will hopefully be targeting with Vilya, though many of them are eagles that Radagast can help pay for as well. Escort from Edoras can be saved until stage 4 to help with the final push. When I beat the quest, I didn't end up needing any healing, but Warden of Healing is there of you need him. He'll make a good chump blocker too in a pinch. Beorn can take out any enemy (except Mumak) in a single turn and I like that you get another chance to put him into play with Vilya.
Part of my reason for publishing this deck is because I didn't find many solo, progression decks here when I was struggling to beat the quest. I hope this can help someone else who is in the same position I was.