The more I think of this, the more I want to homebrew FATE to do this. (Or maybe FUDGE).

Ignoring the class part - the truth and about souls-like game is that death is very real...and also somewhat meaningless. When you die, you just reappear again and just have to do it all over again. The "fun" is the "what do I have to do to finally beat this stage/boss". Unlike in most trad ttrpgs, where death means something, in FATE "losing" doesn't have to mean death. You can insert whatever fictional reality you want as to how the characters become displaced and/or what the enemies do vis a vis the defeated PCs you want.

And, because FATE is very hackable, you can hack/homebrew whatever additional crunch/tactics you want on top of that chassis to get what you want. Want to add a subsystem of "damage" before instituting stress? Do it. Wanna add different fighting skill trees on top of what's in "vanilla" fate. Do it.

While it's inherently narrative-leaning, it's also crunchy enough to make it crunchier. It also doesn't care about verisimilitude, so you can insert only the kind of crunch you care about. Super flexible.