The obvious solution to me is to allow archive.org access on the agreement that they archive it for later access. Give newspapers, like, a month before giving access to everyone to the archived article.
Part of the purpose of archives is to hold power and everyone accountable. Webpages can change at will with no history, so if you can't archive at will you're losing out significantly.
Archiving at will would be kept, the change would be in archiving the pages internally for some time and making the captured articles public later.
Ah, that's cool. I'd love to see some competition to archive.today
Related discussion last month:
Tell NYT, Atlantic, USA Today to keep Wayback Machine