I’m going to stay a little vague on the rest, because anything I describe in detail here is something a publisher can patch by Monday. The general idea is to treat each site as its own problem: several methods per request, a check on whether the article actually came back (not just a teaser), and on to the next method if it didn’t.
On archive.is: yes, the CAPTCHA is the annoying part. Volume is low enough that it’s manageable, and it’s a last resort rather than the main path.