I just managed to finish this as well. Having recently completed the Angmar Awakened cycle for the first time, I also had to go with a Vilya deck as that was the only deck I was able to get a win against Carn Dum with! I built the deck a while ago before I had a larger card pool so I probably should have optimized it a bit, but time got away from me this month. I was able to get through the quests with 6 total tokens which I was pretty happy with. I posted over on BGG, but I am the only one over there so I will post here as well. Also, I am not able to get access to the spreadsheet aside from "View Only".
The Dread Realm - I started in reverse order since I know this deck beat Carn Dum at least once but lost to Dread Realm in its one attempt in my cycle playthrough. My first game was awful. I drew Heavy Curse in setup which surged into another Heavy Curse so I had two sorceries attached to the quest before I even started!! I just decided to scoop and take a token on that one. Then, on my first token game, I completely forgot to take it. Probably because I lost the first game so quickly lol This run did not go much better anyway as I could not draw into any allies. It was not long until I had a host of enemies engaged with me and nothing I could do. Finally on my two token run I had a breakthrough. I got Treebeard and Beorn out quickly and got very lucky with the encounter draws being locations I could travel to and clear so I had some time to get set up. It still took me a few rounds but thankfully no treacheries came out and when I finally got to Daechanar I was able to take him out quickly with Beorn's action and a few other heroes/allies. Then I drew into Faramir at the perfect time to make one last huge quest push for the win.
The Battle of Carn Dum - Well this went about as good as I could have hoped with me getting out of it with 4 tokens. The first couple of games I could not draw into Vilya or any allies. The encounter deck was throwing loads of enemies out at me too so it did not give me any time either. In my 4 token game I was able to get Quickbeam out to start helping with questing as well as Light of Valinor and a Shadowfax so I was able to quest and ready with both Glorfindel and Gandalf. A combination of Lembas and Miruvor on Elrond allowed me to defend multiple times with him as well once a lot of enemies started coming out. Treebeard and some 2 willpower allies sealed the deal and I was able to quest through Stage 2 quickly and then take care of Thaurdir.
The Treachery of Rhudaur - I did not think this one would give me trouble, but it was actually a bit of a challenge. I did not get Vilya right away and had to tread water for a little bit. I did not get any clue cards which made the next stage last another round longer than I would have liked since it required the full 30 quest points. Thankfully allies became plentiful and I got enough questing. I had some enemies engaged with me I had to defend before I could get to Thaurdir though and one of the shadows was an undefended attack which took out Glorfindel but I still had enough to kill him in the end and get through with 0 tokens for a grand total of 6. Definitely a tough trio of quests!