That's exactly what I configured right after reading this news, here's a rule I came up with:

(https?://www\.nytimes\.com\/\d{4}\/\d{2}\/\d{2}.*)|https://archive.is/newest/$1

Unfortunately, I quickly encountered the "Too Many Requests" error while testing. Maybe I should configure an nginx rule to distribute requests along my multiple VPSes to mitigate this...