The first order of business--before the draft--is to trade Ullmark, Coyle, and Zacha, and then sign or acquire 2 new centers for the first two lines. I would go for Lindholm and Monahan first. They could also get a center for Ullmark, but we'll see what he brings.
They need a LD to pair with McAvoy. I admit that I'm heartbroken that Hanifin is off the market. Maybe Zadorov, but there aren't a lot of great options. I suppose they could sign a short-deal with an older UFA, in order to buy time for Lohrei to further develop. I'm not comfortable with him on the first pair.
I'm not adverse to re-signing Nosek, who is excellent at the PK and on draws. Our face-off performance has been no less than dreadful this entire season, and it's got to change. Derek Sanderson, who was great on face-offs, once said, "If you control the face-off, you control the puck; if you control the puck, you control the game." Lindholm is great on the draw.
I would re-sign UFAs Jake and Heinen. I would let Looch, Griz, Forbert, and Shattenkirk walk. I'm undecided about Maroon and JVR. Swayman, Boqvist, and Lauko are RFAs, and I would re-sign them.
I'm not against starting Lohrei, Potras, and Lysell in Providence next season, and then bringing one or more up after the season starts and injuries happen. Lohrei makes too many mistakes, and Potras needs to get much stronger; maybe he can do in the off season.