A lot of people from the southern U.S. seem to think May is late spring and September is early fall everywhere. May is generally not spring in the Rocky Mountains, which includes Rocky Mountain, Yellowstone, Glacier, Banff, Jasper, and Yoho National Parks, among others, and mid-September can be the beginning of winter, not fall, in some of these places (I once used a mid-September photo we took of Bow Lake in Banff NP on our Christmas card because there was a foot of new snow covering the evergreens and the surrounding mountains).
The NPS struggles every year to get Trail Ridge Road through Rocky Mountain NP plowed by Memorial Day (most years they fail). The Going-to-the-Sun Highway in Glacier NP doesn't open until about the first of JULY (not June) every year and closes again after the second weekend in September. And there is a good reason (your protection) that Parks Canada doesn't open that difficult, switchback road to spectacular Takakkaw Falls until June.
Maybe, as Gary says, you'll get lucky and global warming will open the road to the falls early this year, but I certainly would not schedule my trip around that possibility!
PS: Just an FYI--bring winter clothes; you're going to need them.