Without having a thorough understanding of the details of their strategy, all I can say is that what they are doing hasn't been working for years now. Watching the Sharks trying to clear the zone and watching other teams attempts, it's pretty clear whatever we are doing isn't working.
The Sharks overly favor the boards up the left side. At one point, they brought the center deep to wind up and come hard in support. They are too single-minded and choose safe more than almost any other team. The defensively stifling opponents have caught on and are waiting for that left boards exit, in force. Even when they brought the center deep, those same teams would designate someone for the center. The Sharks need to use the right and weak side more often. They used some middle to start the year with direct passes to the skater taking the center role; they aren't doing it much. Center deep wind up requires skating and is best done by faster skaters. Fast isn't the Sharks. I have watched Goc do windup for ages and he is really good at it. There are many centers who are. Gomez used to be a king of it.
The Sharks have tended to take the safe way on defense and breakout strategy generically. There are a lot of details. They are quick to use the hard around under pressure. A lot of d to d in prior years as well. They have relied heavily on using the left side boards for their exits. It ends with a lot of pucks getting out but just coming back in shortly after they change lines.
One of my issues with Vlasic is that he comes up well defensively but leaves the hard work to the next pair as his outlets are that poor and he falls back on the hard around/up the boards far too much. The eyeball test for defenders in this regard is to watch them select their escape, skating or type of outlet, and see how quickly they arrive at their decision relative to their brethren on the blueline. See if they look ahead before they secure the puck. The look ahead is what gives many an advantage for the decision that will come less than 2 seconds later.
The look ahead is big for ANY player. That is one of the things Ii notice most about great players ..they seem to always have their head on a swivel. The Joe's are really good at this.