Without knowing details about where you’re hunting, I’d recommend flying. I’ve done the drive a couple times and it’s still cool, but for a hunt focused trip I think it complicates the trip more so than simplifies.
You’re talking an additional 6ish days dedicated to travel you wouldn’t need if you flew, have to worry about meat care/shipping for the return trip, and getting a firearm into Canada almost guarantees a shakedown and unneeded stress.
I didn’t even want to do the conversion math on gas when I drove through Canada this summer at some of those remote stations, so I don’t think you’d save all that much money taking your vehicle vs flying. Plus, if you’re thinking of executing a Haul Rd trip the wear and tear on your vehicle can be significant depending on road conditions, which seemingly vary from week to week. U-Haul isn’t allowing their vehicles on the Haul Rd anymore (people will still do it, with increased risk), but I’d still recommend finding a Turo deal and executing any remote travel with a rented vehicle over the one you need to get back to ND.
Any caribou country north of Fairbanks is going to be stunning, and I doubt anyone leaves feeling shorted on the views if they flew. Tip from a local, don’t confuse good weather with good road conditions. Most people up here would prefer to do the ALCAN/Haul in the winter as the snow/ice covers most of the pot holes destined to ruin your day. Happy to talk more about the trip over DM. Regardless of how you get up here, leaving will be harder after seeing Gods country.