I was thinking about using an existing blockchain such as Bitcoin. Of course then the inconvenient is that archive.org would have to pay a fee every time they submit a new hash. A comment above pointed out that the scheme I described (unsurprisingly) already exists at https://petertodd.org/2016/opentimestamps-announcement

Realistically it might be overkill though, simply setting up some mailing list where anybody can subscribe and be sent the checksum every day or even just publishing it at some URL and letting users scrap it if they want might be sufficient. If we're talking about one checksum every day it's only a few kilobytes every year, it shouldn't be too difficult to convince a few hundred people and organizations around the world to mirror it.