The way to appease the blue collar wing would have been to pick the most popular blue collar capo as Underboss. That's what Paul did in having Neil as his underboss. But once Neil was out of the picture, Paul abandoned that formula for what I do not know. Paul could have called Gotti (or Jimmy Brown as PB suggested) aside and made a deal with him to make Gotti Underboss, and then promise Gotti no retaliation if he turned over the tapes. Then Gotti would've run the blue collars and Paul would've whacked Quack Quack.
Agreed, if Castellano had a little more political acumen he would have kept Gotti sweet and offered him a top spot, if only until he could have safely taken him out. "Keep your friends close and your enemies closer." Always grudgingly admired the way that Profaci cleverly neutered the Gallo's by winning over their support base, such as the Persico's.
Or alternatively Castellano could have appointed James Failla as PB said.
