My logic has always been this:
Marc Staal is f***ing terrible. He is one of the worst handful of regular players in the game. He's just awful. If you buy him out, you save his cap hit to use on other needs, AND you significantly improve the team even if you just sign some stop gap for $2M-$3M. He's that bad that basically any remotely competent NHL defender is an upgrade.
Then, in goal. The different between Georgiev and Lundqvist, to me, it's not much at this point. Of course Georgiev has more upside and is probably more capable of putting on a clinic on a given night, but he has his fair share of absolute clunkers. If you trade Georgiev and use Lundqvist as the backup, whatever possible downgrade exists there is more than offset by the upgrade of replacing Staal with a burned out Lincoln Continental.
So for next year, I think you're better with no Staal but Lundqvist than you'd be with Staal but no Lundqvist. And then it becomes a becomes a wash the following season.
It's somewhat predicated on what you could get for Georgiev--if the best offer is like a fourth round pick, then it's probably not something to want to do. But if you get a good offer, take it and get rid of Staal and improve yourself immediately.
Also, I do have reservations about dumping Lundqvist like that. It has nothing to do with "New York being different" or whatever you've said, I just don't like it when teams dump their franchise players like that. It's one thing if the guy's contract ends and you don't re-sign him and he goes elsewhere, but I think it's different to cut him or whatever. Just my opinion. Obviously the team comes first, but I actually think it's better for the team to keep him another year and buy out Staal, so it works in my mind. I won't be pissed if we buy out Lundqvist, but I'll never feel good about it.