I think if anyone thinks there are easy answers to improving this team, and that they have those answers are really fooling themselves.
The first problem is that we as fans do not know what has been going on behind the scenes for not only the first 9 games of the season, but for the pre-season, the 2012-2013 season, etc. So we're really shooting in the dark with "guesses" as to who are the problem pieces of the roster because while watching all the games is great, to formulate a truly informative answer, we would need all the facts.
That being said, here are a couple of my high level "guesses":
1) Against the grain of HF - Do not fire Noel. Reason? While it may be easier to fire 1 coach over 23 players, I would rather not make decisions because they are easy. Maybe Noel will need to go at some point, but 9 games in? And who do we get to replace him? There isn't anyone in the org that can step in and take over the "interim" tag. If we're going to go in a new coaching direction, wait until the offseason and do a proper search and interview process.
Plus, let's pretend that the issue with the Jets right now is really the effort level from the players. Sure it's on the coach to get the best out of his team, but at the professional level, it's really a lot on the players. So if the problem is really player effort and intensity (something Noel is publicly asking his players for more of), and the org decides to fire Noel, what does that say to the players? The players weren't working hard enough, the coach asked them for more, they don't respond, so the coach gets fired? Ya, that will sure scare the players into playing harder. Now if it's an X's and O's thing, that's different, but this isn't Noel's first rodeo. He's been around some of the best in the business (Hichcock, Trotz, etc), and they all say Noel is a great coach (I know they are not really going to publicly insult him, but they also don't have to give him glowing reviews either which I have heard).
2) Identify who the guys are that are not giving 100% effort every-night: Easier said than done for sure. I am hoping that if I was in this role for the last 3 years, that I would have a pretty good idea who the guys are that bring it every night. On the ice from my fan perspective, the only guy I can really say that about is Kane. Ladd was pretty good in this regard last year, but hasn't had a good start this year. Frolik looks to be a pretty consistent performer, but other than that, I don't know if any other forwards really bring it night in and night out. Little and Wheeler are extremely streaky it seems, and Seto as well. Not sure if the bottom 5 is really the problem right now (not that we couldn't improve there though).
3) Move guys from #2 that are not giving it 100% every game. Not looking to move these guys for nothing, but these would be the "culture" guys I would move. Even if those guys are identified to be Little and or Wheeler. Trading Little would be a bad move position wise and we would then be laughably bad down the middle, but maybe we would have to do that to get better in the long term?
4) In a general sense, try to create a more accountable system within the team - I'm not sure how these things are run behind the scenes (I don't think anyone here does), but I'm referring to practice, film review, evaluations, etc. Maybe start using some of the advanced stats stuff and plastering all that info on the locker room walls. Make the guys who are not performing have to see that info in front of everyone. Start trying to track some hustle / team play type stats. I don't know how you would do this, but some sort of system that tracks and identifies which guys are doing everything they can and leaving it all out there to win. I also don't know how the team does video sessions. Do they just have the video guy edit a whole bunch of selected clips for review? Time permitting I would want these guys to sit down as a team and watch these games from start to finish. Pause the game every-time there is something to discuss, and make players explain and be accountable for lack of effort situations. Want to float? you better be able to stand up in front of the team the next day and explain what you were doing on that play.
5) Keep trying to instill the "Team", "Family" culture: While trying to instill the accountable system, I wouldn't want to go to far and have anarchy and finger pointing within the locker room. To win we're still going to need guys to go to war for each other, and that isn't going to happen without a good team culture. I think TNSE does do work in this area, I just wanted to add it because I don't want to lose it by also focusing on the accountability aspect.
Those are some things off the top of my head from a high level managerial perspective. As I mentioned, it is tough to know which guys to move without knowing what is going on behind the scenes.
For a purely fun exercise though, here are some "guesses":
Agree with Bob E (and others) that we are going to need a #1C. We most likely won't get that "franchise" 1C, but we need something. Unfortunately, a team in the Avs that "might" move a C, would really want a guy like Enstrom. So if we move Enstrom, we need to then find another first pair LHD.
We could move Buff if the org decides that Buff is not a core piece going forward. The Flyers and Rangers seem like places that could offer nice pieces back.
I would look to improve the goaltending situation. The Ducks have goalie depth, I would inquire about a guy like Anderson. See what it would take to get a guy like Hiller or Halak as a UFA in the off season. Maybe inquire about Reimer as well in the offseason.
UFA players I would target would be Orpik, Klesla, Nikitin, Emelin (need a LHD if we move Enstrom), Stastny, Steen.