Different excerpt styles per category, but chronological

You’re on the right path. You can add classes to your content in the loop based on the terms assigned to each piece of work. For example,

<?php if( has_term( $term, $taxonomy, $post ) ) { $work_classes="big-item"; } ?>
<div class="<?php echo $work_classes; ?>"> ... </div>

This only adds the class big-item when the taxonomy term exists on that post. To get has_ter to work, fill in $term with the slug, $taxonomy with the taxonomy slug, and $post with the post id or object.

More information: https://codex.wordpress.org/Function_Reference/has_term