> What I can see, and I don't know if it exists yet (a quick search suggests perhaps not), is some build task that will check all links and replace those that are broken with links to WayBackMachine

Addendum: First, that same tool should – at the time of creating your web site / blog post / … – ask WayBackMachine to capture those links in the first place. That would actually be a very neat feature, as it would guarantee that you could always roll back the linked websites to exactly the time you linked to them on your page.