From what I know, you can't camp at the designated Westwater campsites for the second night. There are one or two campsites where you can camp on River L down below the official permit-regulated sites. They're not far above the takeout.
If someone's got better info, please post.
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