Sounds like a fun trip you're planning. However, you can only spend one night in the standard campsites on Westy.
Unless.... there is a campsite where you can camp a second night but its less than about a mile above the takeout on River L and its in a pretty boring location and has no shade or beach. You've got to scramble up an 8-ft bank to get to level ground. It helps if you know just where it is ahead of time.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse