One trade possibility that might make sense in some ways would be for the Sox to send Jackie Bradley to the Cardinals for Jedd Gyorko.
I like Bradley a lot, but Jedd does hit LHP, plays just about any infield position pretty well, and can't seem to get regular at-bats in St. Louis. In Boston, he could probably take over 2B right away.
In St. Louis, Bradley (0.0 fWAR) could push ultra-disappointing Dexter Fowler (-1.3 fWAR) to the bench and give the Cardinals an elite defensive outfield of Ozuna-Bradley-Pham.
Money is not an obstacle here, as Gyorko's AAV is about $6.2mill and Bradley's salary is $6.1mill. Gyorko has one less year of control, but does have an option for that differential season at $13mill with a $1mill buy out. Bradley might be making close to that in his last season anyway.
However, this would leave the Sox with a lesser defensive outfield of Martinez-Benintendi-Betts and a big question mark about who steps in to DH (or LF/CF, if Martinez stays put)...