Sell and rebuild, but also find pieces that fit.
Buchnevich absolutely has to get dealt for a first at the draft. Whether that's 2024 or 2025 doesn't matter. If he's not getting a first or a blue-chip prospect, it's a wasted trade.
One - or both - of Krug and/or Faulk have to be traded. I'd even add Perunovich or a lesser prospect to a deal as a potential sweetener for Krug. Faulk is still talented enough that you may not have to package anything with him. Get the right team, and maybe you could get something else.
I've seen enough of Hayes. More than enough. He wasn't even worth the sixth we gave the Flyers for him. I don't know what you can get for him, but he can't be on this team if you hope to build the right way. I don't know if you buy him out or what, but I've seen more than enough.
Binnington should be a tradeable option, but I wouldn't do it unless I was absolutely blown away (I'm talking majorly blown away) with an offer I couldn't refuse.
Don't trade Saad or Schenn. You need some veteran players who know how to win on this team aside from Thomas and Kyrou, especially if you're trading Buchnevich for a first. You can't field a team of younger players and expect to succeed at building a culture; look no further than Ottawa or Buffalo.
Definitely sign at least a middle-six center and a veteran defenseman in free agency. The center is non-negotiable; Hayes failed miserably, Schenn's not good enough anymore, and you can't put Dean in a horrible situation by throwing him deep into the fire one year after his AHL debut.
My dark-horse choice for center would be Jesperi Kotkaniemi (if he's bought out by Carolina - which is a possibility if they like Kuznetsov and want to re-sign him and Guentzel). Could be a solid middle-six center who won't look nearly as embarrassing as Hayes, has been around a team with a solid culture in Carolina, etc.
Defense is a little trickier. I'd go with an older, more established defenseman, like Skjei and maybe even Dumba on a one-year deal.
Re-sign Gaudette, Ellis, Dickinson, and Alexandrov. Those are the main ones. I really want to see what the first three can do (with Dickinson another year removed from his injury and especially Ellis, who put himself back on the prospect map), while in the case of Alexandrov, he should be cheap depth.
Nail the draft. We have five picks in the first three rounds. It could hopefully be six with Buchnevich, or maybe even more if you trade out of the first round with that pick. (Thinking the newly-minted Salt Lake team might try to take a chance on Dean Letourneau - considering BArmstrong's affinity for bigger players in Geekie, But, etc., it's a possibility - and trade up for their high second and an early third. All depends on whom we get the pick for Buchnevich from, but let's assume Carolina.)
Michael Hage is my first-round pick. I don't think we move from #16, but I don't like the options for defense there, and I think Hage is the best player on my board. Maybe a guy like John Mustard or Aatos Koivu could be an option with one of the seconds. Other than that? Defense, defense, yet more defense, still more defense.