We used to spend many a week/long weekend covering the areas you speak of in the 90's and typically doing it as a loop.
FWIW: You will likely find heading east from Jasper to Edmonton very laborious and feel long versus going from Edmonton west towards the mountains. That's how we prefer to do it now having done east to west once and hitting Edison and saying "this feels like it's taking forever".
It is not hard to do a loop of Hwy 2 to Edmonton (1.5hrs from Red Deer), West towards Jasper, then south towards Lake Louise, Banff etc. We never slept a minute the one time we stayed at Lake Louise, and left, with match sticks propping eyes open after the first night due to the train noise. You might prefer Canmore and it's surrounds moreso than Banff, but for sure all are worth a quick look see on the short trip you have here as you are passing by. You will come down the Icefields Parkway, worth a short stop/look see and read as it is receding more and more over the years.
We personally like Johnston Canyon area as well IIRC it's off Hwy 1A that kind of arcs from Transcanada and we find much prettier.
Enjoy, we are truly blessed to have such breathtaking scenery to our west.