You have a lot of options and not a lot of time. All the Parks you mentioned are beautiful and have fantastic backpacking. I'd also add Grand Teton NP (Teton Crest Trail) to your list. If you want to backpack, and not just drive from place to place, I'd narrow your trip down to one or two areas - not attempt to visit all of them this time around. If the Canadian Rockies - go to Waterton, Banff, Jasper, Mt. Robson. That's incredibly beautiful and you can do several good backpacking trips there. (Get the book, "Don't Waste Your Time in the Canadian Rockies.")
Alternately, Yellowstone and Grand Teton NP and the Beartooths - Bechler, Electric Peak, Shoshone Lake in YNP and Grand Teton NP, the Beartooth Highway and hikes out of the southern Lakes in the Beartooth Wilderness.
Or just visit Glacier and Waterton - almost any of the trails in those two parks is incredibly beautiful. Or you can follow the CDT and GDT through both parks.
If you do National Parks you have to deal with permits and reservations. You can generally get them on the spot, if you are flexible. There are also lots of dayhikes possible in all of the parks. In the Beartooths or the Wind River Range in Wyoming (south of GTNP) you don’t need reservations.
_Ginny_