There's really no reason to use JDM as anything but a DH while he's here. It's easier to find a Mitch Moreland type than to find a guy who's a worse defender than JDM and a comparable hitter.
If I were the Sox I'd be taking a long look at Justin Smoak, who has always hit well at Fenway, is a respectable defender, and will probably be a bargain coming off a meh season driven at least somewhat by crap BABIP luck and injuries (his xWOBA/wOBA this year: .366/.324). He's not the kind of guy you build around, obviously, but he could be a good cheap bounceback gamble.
If I were the Sox I'd be taking a long look at Justin Smoak, who has always hit well at Fenway, is a respectable defender, and will probably be a bargain coming off a meh season driven at least somewhat by crap BABIP luck and injuries (his xWOBA/wOBA this year: .366/.324). He's not the kind of guy you build around, obviously, but he could be a good cheap bounceback gamble.