Just off gut instinct (I haven't taken the trip for a few years now), I'd think that leaving AK by mid-September would be pretty safe for snow issues....and I believe if one is flexible in routes, once at Whitehorse, one could start looking for the least "snow-likely" route and be even more likely to avoid serious snow. I believe that going into BC one can stay ahead of the inflection point of the "It's snowing / I'm further South" curve by heading South / West ....but again, fading memory.
Unless things have drastically changed, though: a late fall / early winter trip is very do-able from a fuel perspective. As noted above, just need to fuel up early and often. Run off the top 1/3 of the tank.