A number of people have done this.
Reading some of the writeups, it seems a substantial exercise in logistics, right down to "trivia" like getting a permit to carry a shotgun (for bears, in case you meet one bigger than you, before you get rescued
) and yes paperwork, more paperwork and then some more paperwork.
Weather appreciation will be vital.
The actual flying is a non-event, I suspect, because a decent GPS should still function although there isn't any map data N of something like 75N, in the common GNS IFR units.
I suspect the HDG mode of the autopilot might produce "interesting results"
But the NAV mode should work OK, though you might need to cross the pole in the ROL (wings level) mode because the AP is still essentially flying a heading when in NAV mode.
Not many singles have that much range though. My TB20 will do 1350nm in best economy cruise, to zero fuel. I've done 900nm flights, but you want a few alternates
Winds could also ruin your whole day. For more range you might want something like a TBM700/850 which will do about 1600-1800nm to zero fuel (and in which the flight should be easy, at FL300+).