The team can be improved, but it'll be tough. The biggest problem (Zibanejad) both can't be moved AND can't be replaced. We only have three top 9 centers and there are none in the entire system. On top of that, Chytil's health issues mean that we can't really rely on him, which leaves us with Trocheck, who should be a middle sixer.
Coaches have tried to get Zib right by just letting him play through it. That clearly doesn't work. The issue with Zib is likely one of two things-- either he doesn't give a shit or he's just buried in his own head with confidence issues. If it's the former, then we might as well burn it to the ground and re-build now, because you can't fix apathy. If the latter? Rather than letting Zib play through it, adding pressure every time he doesn't get it done, they should slash his responsibility for a stretch. Pull him from PP1 in favor of Laf. Have him focus on a shutdown role with PK time. Get him right with that and THEN start to increase his responsibility.
As for the defense, Trouba needs to be moved. He's a distraction and he's easily replaceable. He's already behind Fox and Schneider. Mancini can step into the 3RD role easily. If we retain, I honestly think we'd get something of value in return. I'd move Lindgren as well. He's a shadow of his former self, and he should be moved for something before walking.
Just like the forwards, though, the pieces that are easy to move don't solve the real problem. Jones is fine as a 3LD, but Miller is the only top 4 LD on the roster or in the system. I'd love to move him (he's not playing great and he'd bring back a haul), but who replaces him? That's an offseason move if he doesn't pull it together.
The team needs a big, defense-first, hard hitting LD to pair with Fox. Then pair up Jones/Schneider and Miller/Mancini.
As for Shesterkin...I'd give him a final offer. It would not be at or above the one he already rejected. If he thinks he can do better, he's welcome to look for those greener pastures. As long as the team has Benoit Allaire, they can get passable goaltending.