FYI, I live in Boulder, CO.
Starting on a coast-to-coast in September is pretty late for the mountains. I've been snowed on in Yellowstone the first week in September. Starting beginning of August would be good.
Otherwise, with your "likes & dislikes", if you don't have your heart set on going coast-to-coast, I would start in Denver (easy to fly here), head up to WY thru Yellowstone, follow the Adventure Cycling "Lewis & Clark" route to the west coast (this is only if you are starting at the beginning of Sept - otherwise you are too late)
OR take the Western Express across Colorado-utah-nevada-California.
Either way, when you get to the coast hang a left and ride the Pacific Coast to San Diego, hang another left and ride the southern tier until you run out of time.
Or if you must go coast to coast, you could ride the Western Express starting in San Francisco, then at some point (maybe around Moab or Durango) head south and pick up the southern tier the rest of the way across.
Or you could ride the Sierra Cascades route, if you like mountains. That's what I'm doing, starting mid-september. All mountains all the time.
FYI, in the USA "backpackers" = "Hostel" and "backpacking" means taking your pack hiking in the wilderness.
I personally think coast to coast is over rated, you constrain yourself to a lot of not-that-awesome riding in order to achieve something that's easy to describe.