Ten hitters have hit .370 or better since Ted - Musial, Carew, Galarraga, Gwynn twice, Larry Walker, Helton, Nomah, Bonds, Ichiro, and now possibly McCutchen. Carew tops the list at .388. That's real close.
I would guess that someone like Ichiro, focused on putting the ball in play and using his speed, with maybe more patience, would have the best chance.