I think you're creating scenarios in your head that you'd like to see play out but these things aren't actually systems.
They just let up 5 goals against Colorado playing in the style you don't like because it's too conservative, what do you think happens when Colorado is getting more chances? Sorokin played incredibly well that game too.
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
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.
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.
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.