Approximately one-third of the route (about 1,500 miles) are in the Yukon. That's a lot of miles to ignore, don't you think?
You guys clearly like the structure of the AK4K -- it's got a nice ring and it's descriptive.
If we keep it descriptive while including the Yukon, what do we get?
"Last Frontier Four-Thousand"
"Wild Yukon Four-Thousand" (in reference namely to the river, which I'm essentially circumnavigating)
Some reference to the total number of road crossings, e.g. "Ten Roads Four-Thousand"