If you say that it's all the same boxes and format anyway, I would create a custom text meta box on the edit page for their posts where they can just type the category (CSS class).
That way they have control in the edit page for which category it belongs to at time of writing (or can easily go back through posts and change without any coding knowledge necessary.)
In the code you can then simply do something like:
$yourclasskey = class //choose the name for the meta_key
$class = get_post_meta( get_the_ID(), $yourclasskey , true );
<div class="<?php echo $class ?>">
Then adjust the CSS to change the style they want depending on the publication.
You could also just use tick boxes in the back and return the values of the class that way??