Mmmm. So we're talking Barrow to someplace south of Ketchikan.
Let me stick my neck out a bit and say that this is not a one-year project. Unlike the people in the linked video, you'll have multiple major mountain ranges to traverse (interspersed with mere minor mountain ranges), long sections of muskeg (unless you're following roads or rail lines, of which there are only a few, this would mean densely-treed bogs), plus large bodies of salt water and major rivers to cross. In summer the weather might be reasonably warm (except at altitude), but much of the way travel is really only possible during the winter freeze, during which it is ridiculously cold (duh) and dark. Stringing together a single complete trip without relying heavily on mechanical transport, deep-pocketed sponsors, and an extensive support system would be beyond improbable.
You're looking for something "really epic." You could pick a segment--say, the St. Elias mountains--and make a major expedition out of it, sell film rights to the National Geographic, and live out your days making motivational speeches to major corporations. You could string together successive trips during the appropriate seasons spread over a number of years and earn a measure of fame for yourselves (and bragging rights for your sponsors). You could even drive the overwhelming bulk of the mileage, use state ferries for much of the remainder, fill in gaps with the occasional bush plane, and call it a pretty damn good summer vacation.
Actually, that last bit might serve you well in your preparations. Why not go there next summer, have a look around, see what you're up against? If it still looks like a go, stop back during mid-winter. You'll want to consider as well the length of time you can actually spend in the US with your visa or visa waiver.
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