I have done two fall cross-country trips - including my first x-usa.
However, both were west to east.
And, I had a moderate amount of touring experience before my first trip.
It's possible to do one east to west starting Sept 1.
But you will have to cut deep into the Southwest to avoid the Rockies.
Also - you never say where you will start and where you need to end.
But then again - there's Amtrak - which is pretty easy for touring cyclists -
Given all the hassles and costs of flying.
One more thing -
An east to west trip in the fall is likely to have a good deal of headwinds.
Rough itinerary -
DC - Blue Ridge Parkway - Cross Tennessee & Arkansas -
Ozark Mtns - Oklahoma - Santa Fe - Grand Canyon -
Sedona - Parker - Joshua Tree - Ventura
8 1/2 weeks - 400 miles per week?? -
66 miles per day with 1 day off for weather, repairs, relaxing, etc.
And don't forget - after Sept 21, the days are less than 12 hours.
Can you do that?
Best - J
Here's a website to give you western temps and precip:
http://www.wrcc.dri.edu/Climsum.html