The odds of you getting over stampede pass during late season is very slim. The snow is coming and it is normally not accessible in late season. Besides, the cats have eaten most of the deer in there.
We used to go in there in the winter with snowmobiles and look at the elk on the airstrip at the old town of Lester. Used to be about 150 or more standing around. Many years ago the cat population exploded and the guys that work the watershed said the snow was all red in the airstrip. They said it was a blood-bath in there. The elk herds dropped really fast and after that, we never saw another elk in there. Then the *censored*s moved the gate keeping people farther away from the town.