The David Ortiz Solution

If I were the Red Sox - I'd solve to problem with David Ortiz in a very simple manner. I'd start have him practice his bunting.

Like the sage Wee Willie Keeler is famous for saying, "Hit them where they ain't." Whenever a team went into a shift on Ortiz - I'd have him drag a bunt down the 3rd base line. If the other team wants to give up the 3rd base line by shifting the third baseman over to short - take advantage of it. After a few infield singles - teams would stop using the shift on Ortiz and suddenly Ortiz would start to have his pulled line drives fall in for hits. Both his batting average and his confidence would rise and suddenly some balls would start leaving the yard too.

This strategy also has the benefit that it couldn't hurt. Even if Ortiz just practiced drag bunting during pregame batting practice - the other team might notice and thus be more reluctant to use the shift during the game.