Best route to Yellowstone from Colorado

I've read just about all I can find on the forum on Yellowstone, and have our plans pretty well set for our trip this summer. But I'm big on planning the trip and trying to minimize time on the road and any unforeseen issues, so I don't want to take the route for granted.

My plan is to leave on Friday after work, and drive about half way, spend the night in a easily accessable campground with hookups for convenience, and pull out early on Saturday hoping to get to Yellowstone in time to set up and do a little site seeing before dark.

Possbile stopping points are Casper or Rawlins (330 and 297 miles away respectively). But these take me two completely different routes, so I'm looking for anyone who has been on either of these routes in the last couple of years and can give me some advice what to look for. The route through Rawlins is shorter (609 vs 669) and quicker (13:05 vs 13:58 per Google). But this route takes me through Grand Teton and into Yellowstone from the south. The Casper route would take me through Cody and through the East entrance.

We are planning a couple of days at Grand Teton at the end of the week, so going through there is not an advantage from a site seeing perspective. I'm just wondering what the roads are like and would I lose a lot of time on the shouter route (traffic in GT and the south entrance to Yellowstone?)

Any advice is appreciated.
(our trip is not till Labor Day, but I had a slow afternoon at work and I'm dreaming about camping - even though we have snow on the ground in Colorado Springs!)
Alan