Here is another factor . Accept the fact that Breslow thinks ( and maybe) the highest IQ guy in the room, not necessarily the best baseball man. He also has a big ego, I am guessing.
The team he put on the field , for whatever reason, worst in MLB through 80 games, half a season . Then, his BOYS came alive and made an improbable run to change the perception. Breslow right now must feel motivated and rewarded by the "process". He will not be a willing seller in bulk because he must validate his earlier judgements .
He will be a buyer if the Sox get to August 1-3 and can maintain position . To do anything else would be to admit it was a bad roster, or use the injuries to Anthony, Crochet, Story etc as an excuse for the season.
Craig will not want to admit anything, so he will try to buy a bat or two, maybe a reliever and hope the Anthony-Crochet team can play . He will let the players on the field succeed or fail .