I think simply modifying the hosts file on a machine to "rename" the domain of the site you want to visit would be sufficient to bypass a browser-level block.
> The browser must send a request with a Host header with the correct site name or the server will 404 it.
Only if you configured it that way. Most http servers have a "default" website which they will happly serve from if the Host header has no match. I expect these sites will continue to work just fine in firefox using the host file hack or via alternative DNS domains.
Unless they just want a foot-in-the-door law to make certain browsers illegal (to then expand on it later), blocking content at the terminal is not the way to do it. So so many ways to get around it.
Please just make the block-list a plain-text human-readable file. That way I can update the file when a new torrent website is convicted and black-listed.
What could work is a local proxy server that translates the host name in the request.
It must MITM the https requests though.