Neil Gendzwill wrote in :

After you're done with Banff, you can take the route in the mountains

I'll leave the US guys to direct you from here. But if I were you I'd
keep going south until I got to Jackson Hole. I've never been but I've
always wanted to go there, hear it's great.

If you follow Neil's advice I would then consider going south into the US
and depending how far east you are, Big Mountain (MT) or if more around
Glacier Park area, there are any number of resorts now in Idaho such as
Schweitzer and of course Sun Valley. In the same area as Sun Valley is
Big Sky, I've been twice and its one of my favorites. From there if I
remember the drive its about 3 hours to Targhee (which has some 'in bounds'
cat riding, probably too tame for you at that point!) and about another
hour or so to Jackson Hole. From there I would drive into Utah. Powder
Mtn and Snowbasin are first on the way and then Canyons and then the
cottonwood canyon resorts (Brighton, Solitude, Snowbird). When you are
done with Utah, which should have plenty of backcountry, you can drive
west and stop in Vegas for a couple days on your way to North Tahoe
(Squaw, Alpine, etc) then down to Kirkwood and what ever other Cali
areas you want on the way to LA.