One data point:
I cycled in mid-August 2016 at peak season. Like yourself, I didn't know exactly when I might arrive. However, I made reservations once I reached Tete Jaune - two nights before. I got a campground in Jasper National Park and found hostels in Hilda Creek and Mosquito Creek. I waited until I arrived in Banff to find lodging there.
My blog page that included riding the Icefields Parkway -
Banff, Icefields Parkway - A bicycle ride across the Americas
Thanks for the Info Mev. That relieves my mind somewhat
. BTW, your link is bad. John