The Atlantic Coast will have rain/thunderstorms that time of year, and possibly oppressive heat and humidity. Not really familiar with camping, either.

You may consider the ACA Sierra-Cascades route instead of the Pacific coast. Usually any rain due to the mountains is showery and if you wait a bit, it'll pass. I do know in California, most of the state parks along and near the route have hike & bike sites with hot showers, which really are a bargain. Stealth camping is also pretty easy along the S-C route, I've done it myself outside of USFS campgrounds that I considered overpriced for vault toilets and no showers (i.e. Lake Almanor).

If I were doing the route myself, I might cut out the more desert Southern California section and zig-zag back and forth across a few Sierra passes instead--really scenic and interesting ones include Yuba, Donner, Carson, Ebbetts, Sonora, and Yosemite's Tioga.

Hmmm--Idaho has some really amazing scenery, big lakes, abundant hot springs and camping, too. Maybe a route could be figured out there, too.