There doesn't appear to be any useful Export options in Okular so can't you print it again to a PDF?

Yes, that is possible. The problem is that what you see in print preview is the lightened image, but what you get when you print to file is the original again.

I don't know how to get the version that Okular displays to print to file.

Maybe I am missing something obvious or doing something wrong. Or maybe the only thing to do is to copy and paste page by page into Open Office, and then export as PDF. It will be a bit tedious but it may be the only way.