It's rare in a game like this to have strong consensus on power level but in LotR I have seen no dissent that Dain & Glorfindel are the best two heroes.

Dain's buff on top of the other dwarf synergies makes them capable of bulldozing most quests. Glorfindel has excellent stats that with Light of Valinor as a cheap Unexpected Courage that lets him quest & attack every turn (or defend if he is desparate). Since he has only 5 starting threat you get the benefits of 2 high value heroes for the cost of one of them.

These seem to be pretty much crutches for all of the top tier lists. So what are the best decks people use without using either of these heroes?

Either suggest  a solo deck or use a pair of decks (or more) that can work together.

I only play thematic decks. Here are a few of my favourites, not using Dain or Glorfindel. All of them are meant for solo but i'm sure they would be very fine for multiplayer too.

Gloin, Nori, Ori = you deckbuild in a similar way as with Dain but with more healing. You'll gain massive amounts of resources.  Another variant : Gloin, Gimli, Ori. You can also replace Ori with Bifur, depends on the way you play.

Elrond, Legolas, Frodo = Many possibilities here. I like to bring in Radagast and the Eagles, works very well.

Denethor, Eowyn, Imrahil = this one is an encouter deck manipulation deck. I included all the cards that allow ED manipulation, including the Secrecy ones (which i make cheaper with the Masters of Lore). Quite fun !

Beregond, Hama, Legolas = my only Tactics monosphere deck that works. Beat Peril in Pelargir and about half of the quests from Mirkwood and Dwarrowdelf with this deck.

Dunhere, Eowyn, Hama = My Rohan deck. It's not exceptionally good but it quests very very well, so it depends on the scenario i'm playing.

I just built a set of three decks based around the Gondor and Rohan heroes the other day. They are built with the assumption that all cards are available, along with a second Core set. Only thing Im not 100% on is that I dont remember how many Galadhrim's Greeting comes in the Core. I have 2 decks marked with 3 each, so if a Core only comes with 2, then the two decks with Spirit would be 1 card short each. :/

I hope these help!

Deck 1: Tactics/Spirit

Starting Threat: 27

Heroes: Beregond, Hama, Dunhere

Allies: 18

3x Defender of Rammas

3x Gondorian Spearman

2x Horseback Archer

3x Westfold Horsebreaker

2x Escort from Edoras

3x Envoy of Pelargir

2x Arwen Undomiel

Attachments: 10

2x Horn of Gondor

2x Citadel Plate

3x Blade of Gondolin

3x Spear of the Citadel

Events: 22

3x Feint

3x Quick Strike

2x A Test of Will

2x Dwarven Tomb

3x Foe Hammer

2x Hasty Stroke

3x The Galadrhim’s Greeting

3x Unseen Strike

1x Will of the West

Deck 2: Spirit/Leadership

Starting Threat: 27

Heroes: Eowyn, Eleanor, Prince Imrohil

Allies: 22

2x Eomund

3x Snowborn Scout

3x Rider of the Mark

3x West Road Traveller

3x Riddermark’s Finest

2x Faramir

3x Guard of the Citadel

3x Gandalf (Core)

Attachments: 11

2x Steward of Gondor

2x Unexpected Courage

2x Blood of Numenor

2x Nor am I a Stranger

3x Cram

Events: 17

2x Sneak Attack

3x Astonishing Speed

2x We Do Not Sleep

2x A Test of Will

2x Hasty Stroke

3x The Galadrhim’s Greeting

2x Valiant Sacrifice

1x Will of the West

Deck 3: Leadership/Lore

Starting Threat: 27

Heroes: Theodred, Boromir (HoN), Denethor

Allies: 21

2x Gleowine

3x Ithilien Tracker

3x Warden of Healing

3x Snowborn Scout

2x Faramir

2x Guard of the Citadel

3x Gandalf (Core)

3x Errand Rider

Attachments: 14

2x Steward of Gondor

3x Dunedain Mark

3x Dunedain Warning

3x A Burning Brand

3x Forest Snare

Events: 15

2x Sneak Attack

3x Mutual Accord

2x For Gondor!

3x Daeron’s Runes

3x Grave Cairn

2x Valiant Sacrifice