If they know they can't keep him at a reasonable price then they should maybe take a run at trying to acquire Askarov in a separate trade since Nashville seems to be comfortable running with Saros. Colorado needs a replacement for Georgiev come playoff time if they want to have a good shot at another cup. I don't know what the Rangers needs are in particular but NY could still come out the other side of this better overall with the right moves. Paying a goalie 11M+ is just not the play.
Some names earning 8+:
Thomas Hertl
PLD
Bo Horvat
Patrik Laine
Travis Konecny
Timo Meier
Mat Barzal
Nurse
Benn
Stamkos
These guys don't even sniff Shesterkin in terms of game impact, yet he is supposed to get paid closer to them as opposed to other game breakers?
There are guys that are getting paid 10+ mill that don't have a single playoff run like his to even get to that contract and he's pushing it asking for 12+ million?
If you don't think he's worth 12+ million name all the players that are clearly better than him in the playoffs, at best you can say McDrai or maybe add in a few other names, so he's what? The 5th best playoff performer currently? Well what is the 5th best salary? It's already 12+million right now, with the cap going up, it'll likely push to 13 and maybe even 14 soon.
The absolute worst case scenario if he wanted to sign a contract on the market would be 11+ million which would be the easiest signing for probably 10+ teams the very second he is available. So is New York really going to haggle over 1-2 million? If so should Edmonton have demanded McDrai stay at around 11 as well so they could get more help?
You make it work for someone like him because the alternative could be infinitely worse (see any of the names I listed or you can see some of the horrendous duds making 10+ million who never accomplished anything close to what he did to even GET the contract, forget about them living up to the contract).