Does Wikipedia really need to outsource this? They already do basically everything else in-house, even running their own CDN on bare metal, I'm sure they could spin up an archiver which could be implicitly trusted. Bypassing paywalls would be playing with fire though.
Archive.org is the archiver, rotted links are replaced by Archive.org links with a bot.
https://meta.wikimedia.org/wiki/InternetArchiveBot
https://github.com/internetarchive/internetarchivebot