My experience with ZZ's is that more come out of the box in a playable and live reed. YMMV. But the reed isn't what contributes to a jazzy sound. Mouthpiece, articulation, and your theory are really what I find makes that work.
I have a premier by Hite mouth piece atm, but that's all you can find around here. I'm just really weary about not being able to test mouth pieces. But I have been meaning to get a new one for jazz.