As a nomenclature thing, perhaps make the tiers Expertise, Specialization, then Mastery? For one, it's a throwback to the old 2e classifications, but I also think it makes a more logical connotative progression... You're good at something, you've specialized in it, you've mastered it.
I agree with ThatDude () about field medicine. What about, instead of being able to heal them, you give them a Cure spell cast at a certain level? Since Greater Restoration is a 5th level cleric spell, what if they options were "Greater Restoration, HP as if a 5th level Cure spell, or revivify plus 2d8 Hit points (i.e. about a 2nd level cure spell)"? That makes everything about the equivalent of a 5th level slot (with Revivfy being a 3rd plus a 2nd level slot), and keeps all the options equal.
As for styles, where your weapon expertise bonuses overlap with fighting style bonuses and feats, consider if there's a synergistic bonus. Does Chopping Expertise overlap with Great Weapon style? What if having both meant you rerolled 1s, 2s, and 3s?