There was a shift when he had a .306 BABIP too.
I think the larger point here, and germane to Crawford, is that the best way to have a higher BABIP that's not entirely based on luck is to hit the ball harder (and higher). Speed is going to help you get more IF singles but hitting the ball out of the IF is still far more desirable (which is why Rojas needs to do it more too).
Schwarber's hard hit percentage was actually up 6% compared to last year., and his average EV was up around a mile per hour. That probably came against LHP mostly too I bet.
They calculate XBABIP now. The difference between that and the BABIP would provide a bit more quantification of the luck.