Good question , hard to answer in reality but try this: DFA ( assumes can't trade) Yoshida for a RHH DH, upgrade from Monasterio ( use a possibly a refurbished Romy G.,), , Move Wong and go with Gasper/Narvaez behind the plate , ,add OF/1Bman to bench. Still will need to make room for Story when/if he returns so maybe Mayer goes to AAA if his hitting stays cold .
So Romy and OF/1B are 2 of the 4 bats , Story and Monasterio's replacement are the other 2. This is not the result desired in terms of adding 4 real hitters but the team still needs to just play out this season .
Note that Casass could become the DH but I truly do not expect him on the team actively until rosters expand in September .