I wouldn't be that hard on the KLR. Fairly reliable and with the 6 gal. tank, you have excellant driving range. Gas stations could be few and far in between fills. One of my concerns would be the comfort of the seat. I was thinking the G 650 GS Sertão would be a great choice too, but then more money. Anyway, Enjoy your trip and come back here and share your experience.
done 4 trips that way..depending on which way you go the long way through St John or through St George towards prince Rupert and turn off at Kitiwanga ( hwy 37) which is the shorter way to Alaska. My preference is that hwy 37as it has quite the scenery crossing 31 trestle bridges which is one way only, so watch out for oncoming vehicles. Make sure your full of fuel before heading up hwy 37 and fuel up til you reach the alcan hwy. You'll find the scenery quite spectacular with several stops along the way. Stop in Whitehorse overnight if you get the chance for a look see around the town as well as the historical aspect of the surrounding area. The only danger you'll encounter is wildlife as there are an abundance of them and I would refrain from riding in the evening or at least take it slow. Once on the Alcan isn't too bad as its all paved as I rode through there when it wasn't and lawdy sakes did I go through tires. Have a good journey .