By that mapped route, you can pick up a lot of time zooming through the midwest, where it's flat and straight. You might consider spending a day
going north when in Wyoming to hit Yellowstone, you'll be fairly close anyway.
the only part that i mentioned that MAY be closed would be yellowstone. i for the most part just made the drive i mentioned. didnt encounter any bad roads at all...
My son went to Yellowstone from Seattle in January, the roads were Ok with 4x4 but you couldn't see much and nothing was open. I would expect it to be OK as early as you are going. We used to go to lake Tahoe every year in October and never saw snow.
right now yellowstone is closed. there is one road on the west side of the park that goes north just inside the boarder, but the rest of the park is snowed in. if he is going through in november, he should be ok. the snow this year is well beyond the norm...
"the path of greatest resistance reaps the greatest rewards"