Just handled the exact same situation as you. You coming to Wainwright or JBER?
I applied for a permit to transport my ammo and reloading components through the explosives regulatory division of the Canadian Natural Resources. The Form is a F04-03C. They're easier to deal with than the ATF. Link to form:
http://www.nrcan.gc.ca/explosives/publications/forms/9939
I crossed the border with about 15,000 rounds, fifty pounds of gun powder, and thirty thousand primers with no issue. They didn't even search the vehicle. I had a very neat folder with all the forms for myself, my passengers, my pets, the weapons I had, and the ammunition.
For your NFA items, you can ship them to yourself, care of an NFA dealer (in the Fairbanks area Bowman Arms or Alaska Illusive Arms are my recommendations). Basically the package is addressed to you, they receive it, don't open it, and you pick it up when you get here.
I registered all the weapons I couldn't drive through Canada with the TMO with the intent of the mover taking them. They showed up and stated they were driving through Canada. I asked to see the permits they had for ARs, suppressors, etc. to go through Canada. They said they didn't need any. I told them they weren't taking the firearms (about a dozen handguns and half dozen ARs, plus a suppressor).
I ended up Fed Ex'ing a huge Pelican case up here to the tune of $700. The transportation office reimbursed me the cost.
The mover may or may not take the weapons (legally or not!). Some movers do not go through Canada, they barge from Washington up to Alaska, some do drive through (like mine).
Any firearms you haul through Canada must comply with Canadian gun laws and be declared on a declaration form, and a fee paid at the border. You can transport some restricted type firearms, but you have to have an ATT (authorization to transport) approved ahead of time.
Any other questions, feel free to hit me up. I PCS'd to Wainwright four or five months ago.
Drive, don't take the ferry. It's a beautiful drive, well worth it. My father-in-law and I did it in three days from Missouri, but that was pretty balls to the walls driving 20 hours a day.