The party's over. There is no magic bullet for fixing this mess. Just getting a new GM and a new coach without addressing the fundamental problems with the team would be rearranging the deck chairs on the Titanic. They will only be able to do so much with this personnel. It's not the system. They don't have the horses to play any other. The system they are playing now is the only hope of winning for a team that doesn't have speed. If they tried to change the system to a more offensive one, they're would get blown out most nights. They don't have near enough players who can run and gun to win against the good teams. The big difference from the Cup years is not that anyone "solved" their system. It was never a big mystery. Everyone knew exactly what the Kings were going to do. That's what makes really good teams really good. You know exactly what they're going to do and you have no way of stopping it. No Richards, no Mitchell, no Scuderi, no younger, still-effective Brown, Greene, Gaborik. That's the difference between those teams and this one.
They need to trade Doughty this summer. Doughty is all-world, but he will no longer be in his prime when this team is ready to compete for the Cup again. That's if he sticks around when he becomes a UFA - which seems unlikely, given where the team is going to be when he is ready to hit the market in a couple of years. Why does he re-sign here if he has no chance at another Cup? He is one of the most competitive guys on the team. I don't see him being satisfied finishing out his career just playing for the money with no chance of winning. You can't take a chance on him just walking, that would be a disaster.
Doughty is still in his prime and will bring a huge return. Trade him along with Carter, Quick and Kopitar (yes, I realize he has a NMC - but he's almost certainly going to waive if he is asked and realizes the team will suck). Maybe trade Toffoli.
You get enough in return for these guys, you can try to package prospects/picks with Brown and Gaborik and still have some picks/prospects remaining. The team is going nowhere with those boat anchor contracts, and there is no way to get rid of them otherwise. If you keep Brown/Gaborik/Kopitar/Quick, there is no light at the end of the tunnel for 8-10 years. If you get rid of them, maybe you shorten that time period by 2-3 years. Yes, the team is going to suck. But it will pick high and will have a chance to get cheap talent with those high picks. Otherwise, it's the black hole for a few years first, and only then the full-on suck. Might as well skip the black hole and get straight to taking your medicine.
Not that I think any of this is going to happen. I think this will play out in the worst way possible because they will still try to play for the few home playoff games which bring in the dollars. In which case, if things go well, we may see a Cup competitive team around the 2027-2028 season.