> Alternatively again, but back to saving websites, surely someone's created a nice tool that will download a page to store it as an archive that won't be broken?

Wallabag[0] does that. It's a self-hosted Pocket-like read-it-later service that strips the page and saves the text of the article in a local database, therefore allowing you full text search right from your own server. It even adds some additional neat features like adding notes to the articles.

The only downside: damn those two currently available themes are awful.

[0] https://wallabag.org/en