Don't go up the coast
In my 20's I made several trips between Alaska and the lower 48 every year. I flew it mostly in single engine planes.
Don't go up the coast. The weather is always bad and there are few options.
I would instead head from Billings to Prince George BC. Then from Prince George to Watson Lake via the trench. Then Watson lake to White Horse. To then be followed by White Horse to Northway Alaska.
You could spend the night in Billings and White Horse or push it all the way to AK in one long day if you wished. One time I left Washington State at 5:00AM and landed in Anchorage at 2:00 AM the following morning in a Cessna 150. Often I would camp. Some of the airport FBO's offer a bunkhouse for those who wish to save money. If I recall it took 16 hours from Seattle to Anchorage in a Cessna 180, 21 hours in a 150 and 26 hours in an Aeronca Champ.
Stick to the bigger airports. Some of the smaller ones that are listed on the chart as public airports are not friendly towns to outsiders. Especially do not land there to sight see or to try and fish the local stream.
I would practice working the term "eh" after each sentence. Example "nice weather, eh?" In addition pronounce the word about as "a boot". As you get farther north clinch your teeth together when you talk. Not in an angry way but try keeping your front teeth constantly touching each other when you speak. Don't move your jaw as you talk and speak slowly.
The weather is very unpredictable and severe along the coast. If you end up flying IFR you will miss out on much of the scenery. I would stick the the inland routes if I were you and never get above 500' AGL. Fly along the right side of the valleys. Don't cruse down the center.
Bring camping gear because Canadian law requires that you carry survival equipment that includes a gun of some kind. Find out that the list is and bring it. They are serious about that stuff up there.
It is a beautiful trip.
Skyhigh