A couple of things -
The timing of your trip should be excellent for opened facilities in the Pacific NW.
As for your questions about lodging -
Campgrounds are usually good about making sure you have a place as others have said -
The National Parks and many Oregon/Washington state parks also have hiker/biker campsites.
Motels along the way shouldn't be too much of a problem, but - -
Lodging near national parks - Glacier, Yellowstone - is often booked and expensive.
(Anyhoo, camping in the national parks is so nice - why do lodges there?)
I would strongly recommend Cape Disappointment at the beginning of your trip unless weather is bad.
Despite its name - it is a stunning place - with lighthouses and magnificent vistas.
If you are squeamish about cycling the Astoria Bridge - you can catch a bus across.
The riding on the Washington side of the Columbia River is sooooo much nicer.
Hwy 4 has very light traffic - US 30 is pretty darn busy - I've done both, multiple times.
Hwy 401 to Naselle follows the river for about 5 miles - fabulous if you are heading east.
Hwy 4 has a few climbs, but follows river valleys thru farming country.
Skamokawa has a lovely campground on the river where it is 4 miles wide.
Then there is the refuge road to Cathlamet.
From Cathlamet you can take the ferry back across to Oregon.
(And you will do a big "Ugghh!" after getting back on US 30.)
There really is no good way to bypass Portland on the L&C Route.
Portland is extremely bike friendly - but it is a big city, nevertheless.
Since you will be going thru St Helens - it might be worth it to stop by the marina downtown.
I have hitched a ride across a half-dozen major rivers - and who knows? - someone may take you across.
There are nice back road that swing north and east of Vancouver if you do this option.
Finally, I rode Hwy 14 on my first X-USA trip in 1987. It has way more traffic now.
I've ridden Hwy 14 a couple of time since and have driven it, too.
Frankly, I find US 12 over White Pass and back roads in the Yakima Valley more appealing.
(Not to mention that it will be cherry season with lots of ripe cherry stands in the Yak Valley.)
Just a few suggestions.
Have a good trip! J