Mid-September, you may get a short storm you might need to wait a day or two to continue. Past the first week of October, storms could be more serious.

I think you are fine if you are moving right along, and as long as you are a little flexible and have budget to stay in a hotel if the weather is bad.

Consider Sierra-Cascades to Western Express, too - a little further south. You miss Yellowstone, which tends to get winter before the rest of the rockies, but gain Utah and get a nice chunk of Colorado.