In the meantime, I'll keep using this handy bookmarklet: https://gist.github.com/n-st/0dd03b2323e7f9acd98e (which obviously only works for pages that are still available; for others, it requires copy-paste-ing the URL).
Also, Google/IA and me seem to have very different definitions of "easy":
> [...] conduct a search on Google as usual. Next to each search result, you’ll find three dots—clicking on these will bring up the “About this Result” panel. Within this panel, select “More About This Page” to reveal a link to the Wayback Machine page for that website.
The only thing that's missing is the "Beware of the Leopard" sign.