I construct tournament-legal 50 minimum card decks.
Then you're making this hard for yourself IMO. There's no reason to build 50-card decks with such a limited cardpool, you'll only end up with subpar decks. JDtA was definitely not intended to play solo with a tournament legal deck if you only have 1 Core Set and nothing else. You'll get that later, when you'll have a lot of expansions.
To beat Journey Down the Anduin solo, I think tri-sphere is the way to go. Théodred + Beravor + Éowyn is a very good team here. I also beat the quest with my best deck so far using Legolas + Beravor + Glóin (I have a 2/2 winning record against Massing at Osgiliath with the same deck, only I used Gimli there instead of Legolas). Both decks have around 40 cards.
Have to say though, I'm not that big of a fan of solo JDtA myself. Not that it's impossible, but it just limits your deckbuilding options too much. You need crazy card draw -> auto-include Beravor + 2 copies of Gléowine don't hurt. Beside Steward of Gondor you'll also need a hero that generates resources -> include Théoden or Glóin. You need heroes to have a starting threat below 30 etc.