Here's a basic plan to fit Karlsson's full cap in 24/25. It requires trading both Marchment and Faksa. Marchment would have 2 years left and a 10 team NTC, Faksa has one year and a 5 team NTC. Faksa might not cost much if anything, Marchment would cost a draft pick to dump unless he rebounds.
These are depth charts and not lines. I'm assuming Pavelski is okay with pushing more of his salary into performance bonuses, and that is assuming he doesn't retire by this point. AFAIK the CBA does not limit bonuses for 35+ contracts. The cap situation the year after is much easier with Benn, Lindell, Faksa all expiring. Optimally, the team would save cap this year to minimize carryover bonus overages. This is tough because Lundkvist and Harley have bonus heavy contracts (not sure on the specifics of their bonuses) as well as Pavelski whose bonuses are basically automatic.
Where this gets really exciting is if somehow one of Benn or Seguin is able to spend the next regular season on IR, this contract can be added without breaking up the band. It's the same core as this year + Karlsson, Stankoven, Bourque. This is kind of a pipe dream because you can't force a player to get surgery, but we also don't know their medical details and they could be putting something off because the recovery time is too long. Well now's the chance!
Even if we can't pull a TBL/VGK the team could always pivot into the first roster for a season. The depth is weak and it probably fails to get the job done, but the roster in years 1 and 3 of Karlsson's remaining deal could be extremely strong.
I haven't considered the assets needed to get Karlsson. That's why Bourque is penciled in. The only prospect given real responsibility here is Stankoven, and I'd guess he's untouchable even for Karlsson. All the contracts I made up are highlighted. This is the opening roster for the season after next. This upcoming offseason would be all about saving cap for Karlsson's partial cap hit and any potential bonus overages. I'm also assuming the cap continues to increase as projected. The main reason this is viable is the post pandemic cap bouceback.