I find that Northern communities in Canada like Stanley Mission are pretty friendly and welcoming. Anyone coming in will be met with curious looks, but they're just people living their day just like anyone else. I wouldn't be too concerned traveling there. Having said that, if you're camping/crossing on private land it's always required to ask permission, and I'd treat the reservations like private land. So either ask permission when camping rough there, or stick to campgrounds.
Banff and Jasper you' can't really go wrong with as a trip. Gorgeous drive up the Icefields Parkway (93).
Sleeping rough in Banff... It is a national park, and if you're going to find unwanted attention you'd probably find it there. IF you're going to do that, park in a public swimming pool parking lot or something public. Park late in the evening, and don't crack out the bar-B-Que for a wienie roast. That's a sure way to get some attention. There is year round camping in campgrounds there... As a suggestion.
If you don't mind getting off the beaten path by half an hour or so, from Highway 1 just west of Calgary go north to Cochrane, and west on highway 1A (It's the old highway 1 and a very pretty drive). Head North a bit to Waiprous on Highway 40 and camp there. It's off reservation land, it's not a park, it's off the beaten path and you'll be sure to find a nice dispersed camping spot. Camp there the first night and head into the park fresh in the morning.
If you just want to crash for a few hours late in the evening park in Canmore. I've done that before and never had a problem.
Sounds like a fun trip!