My goal here is to get a sense of "leveling up" back into Fate without having skills and stunts reach ridiculous levels. At the same time, I want to see if I can get a stronger distinction between classes. So:
Class AbilitiesYour Class can and should be represented by one or more aspects, but beyond that your Class is an Extra. It works like a skill pyramid made up of Class Abilities, which are stunt-like shifts of effect. At level 1, you get a single shift of effect, named appropriately for your class. A Fighter might have "Power Attack +1" or a Wizard might have "Magic Missile +1". At level 2, you gain another +1 ability. At level 3, you can either have three individual +1 abilities or one +1 and one +2. A +2 ability costs 2 XP (or whatever we end up calling the resources used to increase these things), a +3 ability costs 3 XP, and so on. The abilities also need to follow a column or pyramid structure, so you can't just have a single +2 ability at level 2; you'd need to "support" that +2 with a +1 underneath it.
6th level Rogue example:
Sneak Attack +2 [ ]; Disarm Traps +2 [ ]
Sneak Attack +1 [ ]; Evasion +1 [ ]
What are the brackets [ ] for? Well, I'm ripping off 2nd edition Fate with some of +Mike Olson's Thrilling Fate hacks. You can use each class ability once, gaining the listed bonus on a roll, and then that ability is exhausted until... I don't know yet. Maybe an "extended rest", but I never liked the weird resting dynamic in D&D myself. Maybe anytime there's significant downtime (your extended rest goes here), you clear all your abilities. Otherwise, you can clear one ability per scene? Refreshing these abilities also seems like a space where you could have other class abilities interact. Maybe the Cleric can refresh his allies' ability pyramids. Maybe monsters have these abilities as well. This skews kind of close to 4e's encounter powers, especially when viewed from the monsters' PoV.
Are class abilities aspects? Maybe? I think they need to have some of the "fictional truth" that aspects have: a Magic Missile can strike at range, a Sneak Attack can't be done if the bad guy knows you're there, and so on.
Are these abilities only bonuses? I don't think so, I think you can use the stunt guidelines. For example, typically I see "hit everyone in a zone" as a 2-shift cost, so you'd need to be a 3rd level Wizard before you can get a +2 class ability. At that point, you could take Fireball. It wouldn't give a +2 to your roll, but you could strike everyone in a zone.
It's a half-baked idea, and there are tons of ways to do D&D murderhobos in Fate, from using the game as written (such as in the Core book example characters) to combining FAE approaches and D&D classes. This way is just how I'd start doing it.