Hiding posts in dashboard list by custom taxonomy.

I’m trying to fix up an existing site that has several custom post types, each with custom taxonomies and lots of existing posts within each of them.
One of their largest post types has a custom taxonomy named ‘archived’. This is a single checkbox for them that the theme then uses to sort that post to the ‘archive’ section of their website. They still want it to be visible to the public, this just lets them move it to a different section once it’s no longer relevant.

However, they have a lot of posts and would like to be able to hide the ‘archived’ posts from the custom post type’s ‘All Posts’ list in the back-end, since they’re not needed to be seen by the admins anymore, and I’m struggling to find a way to achieve that.

I can find plugins such as this which will let me filter and only show the posts which *have* been archvied, but I need the opposite of that. I can find posts that create an ‘archived’ status, but they remove the post from the front-end as well.

Does anyone have any recommendations or suggestions?