Creating a full-fledged offensive system at the NHL is a full time job and takes planning and and an understanding of the roster you have in front of you. This is beyond your and mine pay grade. What I offered you are indeed scenarios that are elements of an offensive minded system a system that appears totally foreign to Lambert but other teams have done it with success through the years. We need a new coach with the experience to implement such a system.
Your suggestions so far include:
Different strategies for different lines.
More dump and chase for the bottom 6.
More cycling for the bottom 6.
Aggressively forecheck for the fourth line.
Cheating for offense from our top 6.
Create odd man rushes the other way.
More defensemen joining the rush.
More drop passes from the top 6.
More skating opportunities from the best skaters.
Create more chances with speed.
I don't have a problem with the criticism, as I previously mentioned, but you're not offering much meat here. Again, that's fine, but you're continually posting like you have all the solutions while simultaneously acknowledging your lack of expertise in the area and being incredibly generic in the solutions you think should be implemented. Saying they need to score more goals and win more games isn't anything insightful (and yes, that's an oversimplification).
How do these things happen? What does that look like?
I'm going to be as clear as I can, I do not have all the answers and I do believe there is more than one way to have success in the NHL. I'm interested in learning more and that's why I'm pushing the conversation a bit. My favorite part of the GDTs or these discussions is when I'm learning something new or seeing the same little things as other posters.
As for those 5 goals against Colorado. As I said that is the result of team that has figured out Lambert's predictable system of sitting back and trying to box out the high scoring areas but allowing the opposing team to get a ton of shots on net. Don't tell me that this is not an element of Trotz/Lambert's system. We all know the Islanders have had some the highest shots against in the league the past 5 years. Eventually teams will catch on and know that the team poses no offensive threat especially when they are focused on holding to a one goal lead and the game becomes a shooting gallery. Against a high scoring team like Colorado or the Devils you are just asking for trouble if you let them get that many shots on net. This is what I mean when I say the Islanders currently play a game not to lose rather than one that plays to win by building bigger leads. The best teams in the league play "to win". This is the primary reason we lost all those series against Tampa Bay and more recently against Carolina. The Isles are taught to hang on for dear life with a one goal lead rather than building on the lead. The best defense is a good offense. Spend more time with MORE players deeper in the offensive zone and keep the shots goal to a minimum and keep the opposing team hemmed into their own D zone.
The Islanders gave up two PP goals because they were trying to be too cute when they were on the PK. That had nothing to do with the sitting back and protecting the prime scoring areas of the ice. Makar's goal was because of a bad line change and bad gap control after the puck was cleared from the zone. Byram's goal was because of a miscommunication about who was supposed to challenge the point. You could make the claim that this is a byproduct of being defensive minded but it's really just a blown coverage. MacKinnon's goal was because Clutterbuck couldn't handle the puck cleanly on the wall and actually kicked it right to MacKinnon in one of the prime shooting locations. Rantanen's game winner came after Pelech had a shot/pass blocked at the offensive blue line and the Avalanche transitioned the other way quickly.
Out of the five goals that occurred before the goalie was pulled maybe one of them could be argued was a systems issue. This isn't an example of teams figuring out the system and dismantling it. This is poor execution of simple things. Making these mistakes in any system will cost you the game against a team like Colorado.
BTW Sorokin is most effective when he can see the puck. All the teams are catching on to the idea that to beat Sorokin you have to have the shots screened. Having all those players collapsing in front of the net is just creates a bigger screen in front of Sorokin. He needs to see the puck in order to stop it. A more traditional offensive minded system will lessen the crowding in front of the net.
Screening goalies isn't knew and isn't unique to Sorokin. I'm a little confused by what you mean when you say "lessen the crowding" because that would seem to imply you're leaving guys open in front of the net or slot and that would be very bad. When cheating for offense usually you're asking your players to initiate a specific route once your team gains possession. If you don't gain possession you can't cheat. That usually doesn't equate to less crowding in front though.
There are several approaches to handling traffic in front of the net. Some coaches want players to try and block everything, clogging shooting lanes. Others prefer their players to not do that so that the goaltenders can see the puck easier when it's coming in. Some coaches want their defensemen to tie guys up, while others want them to be a bit more aggressive and try to remove those players from the front of the net. Which side of the player you're on is also a factor (inside position vs outside position). Lastly, switches in the defensive end are also hugely important and I think the Islanders struggle knowing when to do that at times.
In regards to how we ended up to where this team is today. Think about this. The Islanders ended up with a conservative, trap based, low scoring system because Lou brought in Trotz the moment he became GM. He didn't build a roster that was necessarily optimized for this system of play he just took the team he had in front of him and basically told the team, "hey guys we're going to totally change the way you guys play the game no questions asked". It's not like this team was built from the ground up to play the current system of play they were essentially forced to because this is the only system that Trotz deploys and everyone knew that. So it didn't matter that you were Matthew Barzal, Pulock, Nelson, Dobson etc... You play the game the way we want you to play it. The problem with that approach is that it could amount to nothing more than trying to fit a square peg into a round hole and in regards to some of our more gifted skaters that's pretty much what is going on here. The players are treated like pawns on a chessboard rather than allowing them to utilize their athleticism and talent drive the play. So players like Dobson, Wahlstrom, Barzal, (and before them Bailey) are playing the game in a way that goes against their natural instincts. I don't think this is the proper way to manage a team.
Lamoriello is a net out guy when building his teams so he brought in a coach who fit that mold. I don't believe Lamoriello told Trotz what to run at all and I think Trotz was able to evaluate the roster and implement the system he thought would work best for these players. He's a defense first guy but always tinkers depending on the roster he has (we didn't run the same thing Washington ran). These coaches have access to hundreds of hours of film, I think it would be wrong to assume they didn't tailor the system to the players they had on the roster.
There's no way for me to convince you that playing a system and ensuring everyone buys into that system is important. You want players to freewheel and do what they want, I don't and think it's detrimental to the team having success. There are obviously degrees of each thing and every player is likely handled a little differently. Someone like Barzal was still new and definitely had to learn to play a more responsible game. Again, if you don't believe that then there's nothing I can say to change your mind.