There are things that are going to have to be set to the side for the hack to work (as others have said). Since I’ve played EarthDawn (nearly two decades ago) I’ll put in my thoughts.
Pick and choose what is important. What elements of EarthDawn are important to you - that you just can’t let go of… And I’ll go ahead and say Torchbearer might be a better fit? Since EarthDawn was really just a way to have a D&D world with built-in reasons for exploring “dungeons” (aka Kaers) and other D&D stuff like character levels.
Keeping the Karma Ritual is totally fine. I mean it was just a way to use XP to buy Karma anyway - it didn’t give Karma, just converted XP to Karma. So I’d just use it as something the players would have their characters do to access their Artha, after they have earned it in the same way as they normally do in Burning Wheel. So then it adds some interesting-neat EarthDawn color.
Disciplines (aka Classes) have to go. You could totally call somebody an “Elementalist” or “Sky Raider” or “Troubadour” or whatever, but again this is probably just going to have to be a color thing. Keep the LifePath system if you are going to use Burning Wheel. So the Village Born > Village Guard > Duelist character is a “Swordmaster”.
EarthDawn Circles (aka Levels) really don’t work. Plus ‘Circles’ is already a jargon-word in Burning Wheel for finding NPCs. I’d just drop the idea of Levels entirely - they just wouldn’t really work - unless you went the Torchbearer route!
The Talents (aka magical skills) thing was always just color anyway. At least that is how I remember it. EarthDawn Talents would be a combination of Skills for some and Traits for others in Burning Wheel. So just describe things like picking pockets with a hint of magic, “the purse is levitated to your [nearby] waiting hand”. And so forth. (For people who haven’t played EarthDawn it wasn’t actually levitation, it was just a way to magic-color the skills - the character still had to pick the pocket).
EDIT: I suppose you could also add in some of the more magic-y skills like, f’rex, Fireblood. I’d probably make it a Trait that allowed access to the Fireblood skill (essentially an instant Surgery use), instead of giving all characters access to spells. Or do something with Thread Weaving (see below) and use a Linked Test from Thread Weaving to Surgery to allow instant use of it.
EDIT: or the more obvious answer would be that magic-skills could act like Elven Spellsongs.
Magic/spells/sorcery: again I’d just color the in-game talk to include Weaving Threads. Spells already take multiple actions in Burning Wheel anyway, so it fits - they are Weaving Threads. There is a method in the Magic Burner that could mimic Spell Matrices, as well as other forms of spellcasting! Sorcerers have to deal with Tax in Burning Wheel, unlike in EarthDawn, keep Tax anyway.
Magic items were neat. I remember all the characters having a Thread Weaving skill to bond to the item - you could keep that if you want to. I’m sure you could do that stuff with magic items and not worry too much. I remember having to do quests to “unlock” the item’s magic and Weave Threads to them - cool stuff.
So, yeah, mostly color stuff in interesting EarthDawn ways is my solution I guess. Huh. Or get Torchbearer and hack it.