My choice would be Ottavino, but I completely agree Barnes will get another shot. If Richards can be rehabbed into a pretty darn good reliever--small sample, just 4 games--Shirley Barnes can. He needs to think about what he is doing and focus on fixing what is fixable. And, exactly as you say, Cora needs to send him back to the mound. I think he should use his changeup more and to throw more pitches low in the zone--or high or above the zone if they will swing.
Right now the Sox bullpen needs reliable arms, and Barnes has one, it's just not quite as reliable as the one we saw earlier this season.