TwoSix
Everyone's literal second-favorite poster
You put the story in the subclasses. And you present the subclasses as the primary layer, even though they’re contained in a larger top level category.These need stories. People don't want 4E that is mechanics first, they want 5E that is story first followed by unique mechanics.
Make classes more like class group in 2e. Shared mechanics and progression are contained within that level, specific diegetic mechanics are at the subclass level (which could be called “class”, if you want, what things are named isn’t really relevant to the design).