Not sure. I did some very far north routes on the 777 back 13 years, but never polar routes. I just remember hearing that some of the routes had only a few alternates and if one went down you had to fly a different route. There are several airports up north of 60 deg. But if one goes down, the next suitable airport might be 70 E or W of that longitude. It might not be apparent to line pilots, as dispatch might give you different routing. I can't swear to this one.

The ETOPS no go areas in oceanic regions I do know about. They never affected UAL until IAH-AKL or SYD. LAX and SFO flights fly north of this area on a pure great circle route. Obviously different wind components could put the best route through this area.