Yep. I understand the problem perfectly, but when I look at DD I see a guy who likes his 'up the middle' defense. This is a guy who's traded for Iggy - certainly not because of his offense! - and has already turned down potential trades for for JBJ.
IMO if he's going to trade away one of our outfielders for pitching it might be Benintendi The upside of a trade like that is that it would improve our pitching staff and, let's face it, LF in Fenway doesn't require good speed or a good arm, just familiarity with the wall. We could improve the pitching staff without badly damaging our OF defense. The downside is that it wouldn't relieve the money crunch.
One of the things that would make Beni marketable is the same reason that the Sox might be reluctant to do it - Beni's contract and team control. But as they say, you have to give to get.