Google Maps says it's <1000km. Easy enough for Canada to put out a RFP, noting "don't bother us if you think it'll be over C$25 billion". That's C$1M for each 40 meters of pipeline, at scale. Maybe you want 6 pairs of footings per 40m? Sounds like it could go up darn fast, with the footing crews working a week or two in front of the pipe crews. (And building it fast also minimizes the supplies you have to haul in & out in an area where, as you noted, you can't lean on local water & sewer & electrical service, and the corner hardware store for a odd-sized wrench you just realized you needed:) Meanwhile, a few Nordic shipyards are building the icebreakers, and another firm is digging the new harbor and channel on Hudson's Bay.
Vs. in mountains - yeah, roads are a big issue there. Because the roads themselves can take years to construct. And still, being a mere 1/2 km from the road isn't much comfort if that is up and down sharp slopes - which will mean soil stability and erosion and pipeline pressure issues, every meter of the way.