I have to agree, the Icefields parkway between Banff and Jasper is spectacular, and worth seeing even if the aarea seems like a real tourist trap.
You could certainly take the Alaska Highway down to its beginning in Dawson Creek, BC. Then its just across the border to Grande Prairie, Alberta, and south through Grande Cache and Hinton and into Jasper National Park. South through Jasper to Banff national Park, and then continue through into Kootenay National Park, which is back in BC. Hwy 3 across southern BC is a beautiful ride out to the coast.
My wife and I rode from the coast (Vancouver Island, actually) along Hwy 3, and through the 3 National Parks and ended out trip in Jasper this year. We thought it was spectacular. We have also done the section from Fort St. John on the Alaska Highway through to Hinton, which is on the eastern edge of Jasper Ntl Park. That was also a great ride.
The ride from the Coast to Jasper along Hwy 3 took us most of the 3 weeks we had for holidays, and I think came out to about 1450km. Going by memory, I think from Fort St. John to Hinton would be about 550 km, and the Alaska Hwy from Fort ST. John north to Fairbanks would be about 2400 km. A little computer work tell me that going this route would be a total of about 4600 km (2875 miles), give or take a couple.
Are you planning on spending time back home in the States for a while, or just a pit stop on your tour? You might find this area of yur trip more remote, and less inhabited than most of the areas you have cycled. Things tend to be quite a ways apart in the north.
The other option is to take the Stewart Cassiar highway, go to Prince Rupert, and ferry down the Coast to Vancouver Island. If you do tht, let me know and I'll be sure our spare room is ready whnen you come through Nanaimo.