I would definitely do the reverse order to insure that all of Glacier NP is open.
Denver then Rushmore and across to Little Big Horn. then over to Yellowstone/Tetons. on the east side of Glacier Aspire we stay at St Mary KOA. Great park just at the east end of Going To The Sun Road.
From the east side you can go to Two Medicine, Many Glacier and Chief Mountain. Going across Going To The Sun takes you to Logan Pass and down to McDonald Lake.
All of these offer the chance of seeing black and grizzly bears, elk, moose and mountain goats. You can probably tell I love Glacier.
We are going there the very end of June this year hoping it will all be open.
Have a great, safe trip.
Ed
2012 Entegra Aspire 42
Jeep Grand Cherokee toad