Weren't Great Britain's Arctic Islands separate of Canada for some time? I don't think the British have a reputation for selling land, but perhaps in an era when Europe was heading for a Great War, the British sell the Russians the Islands as a token of good will?
This will add a very new interesting angle to the Russian Civil War if it occurs.
In addition, perhaps the Russian's could have also partitioned N.W Territories with Canada, and few bits of Rupert's land for a straight border (This would be needed if we are strictly going for the entire Arctic Circle being Russian).
Greenland could also be taken if Germany bullies Denmark into joining the losing side of World War I equivalent.