The fastest driving route is Jasper - Clearwater - Kamloops - Hope - Vancouver. It' 800 km. Map Quest gives the driving time as 9 hours (not counting stops), and Free Trip gives a time of 8 hours. I'm a fairly cautious driver, and I find that my actual driving times are consistent with Map Quest's.
Between Kamloops and Hope you drive on the Coquihalla Highway (Hwy #5), which is a toll road (C$10 per vehicle).
Hardly any of this route will overlap with the Rocky Mountaineer's route. Although you will have gone from Vancouver to Kamloops on your eastbound journey, the railway line will more or less have followed the TransCanada Highway's route through the Fraser River Canyon (via Lytton).
You can see the route map if you go to the Map Quest website and plug Jasper AB in as your starting point and Vancouver BC in as your end point.
The overnight train trip to which jerm referred is the one that VIA Rail offers. It runs on the same track as the Rocky Mountaineer's "Yellowhead" train. However, unlike the Rocky Mountaineer, the VIA Rail train does not stop in Kamloops for the night, but keeps going. VIA Rail departs from Jasper 3 times a week. It departs Jasper at 3.30 p.m. and arrives in Vancouver at 7.50 the next morning (for a travelling time of 17 hours 20 minutes). Around the middle of September sunset will be somewhere between 8.30 p.m. and 9.00 p.m., so you'd have a good 5 hours in which to scenery before night fell.
Although, as jerm said, flying from Edmonton technically would be the quickest way of getting to Vancouver, it wouldn't be THAT much quicker than driving. Since Edmonton's Airport is well to the south of the city, I think Jasper - Airport would be more like 4 hours. Then you'd need to allow an hour for checking in for a domestic flight. Then the flight would take 1.5 hours. Then it would take 30 minutes or so to retrieve your luggage. Then a cab ride into downtown Vancouver would take about 30 minutes. So I make that 7.5 hours from Jasper to downtown Vancouver.
Please see my response in your other thread on the same topic:
>>>>>>Please see my response in your other thread on the same topic<<<<<<
LOL, jerm, sorry about that. When I couldn't see my response below your two responses, I thought either my computer to TripAdvisor's website had the wobblies. But, here it is.:-)
>>>>>>either my computer to TripAdvisor's website<<<<<<
I meant, my computer OR TripAdvisor's website." Arghhhhh.
Driving time depends on season of travel. Winter travel should slow you down most of the time and even delay due to avalanche control or highway closures.
Destination is also another big factor. "Vancouver" is a big area. Do you mean downtown, airport, ferry docks or some suburb of Vancouver(ie Surrey, Langley, east Van, north Van...etc). Perfect driving conditions to the extremes of Vancouver would be in the 9.5 hour range if you know your way around traffic and the town.