We crossed this year at Sweetgrass, MT on May 10th. Went on to Banff, Jasper, Lake Louise, and then Alaska for about three months. WE did NOT make reservations anywhere and only had one night that we could not get into the Russian River National CG due to huge fishing pressure and lots of campers in that area.
Wing it. No problem. No stress.
A little advice, probably not a good idea to drive by any open fuel station on the Alaska highway if you are close to 1/2 or even 3/4 of a tank of fuel. Less stress of a running out situation this way. If you drive a POV that gets 25 - 30 mpg or an RV vehicle with auxiliary fuel storage, this advice does not apply.
Have fun and safe travels.
Lakeside