Screw it, just get both of them then. EE is clearly the better hitter so you sign him as primary DH for one year. Castellanos is your regular RFer. That leaves you a little light on LH bats in the starting lineup, but you have Mazara and Collins coming off the bench as LH hitters.
We know JR and the Sox are never going to spend 300 million dollars on top tier elite FAs, but maybe they will be willing to spend some money on moves like this. EE's money will be off the books after one year, and Castellanos's contract shouldn't be too large to be a real albatross, and he'll also be off the books when it's time to extend some of the core guys.
I say be a little bold for once and make a splash by signing both.