I finally found a way to do this, although it’s not anywhere close to ideal. I ended up editing the existing theme widget, which they don’t recommend and will be overwritten whenever the theme is updated, but I wanted something working for now.
So I edited wp-content/themes/LivingOS_Xi/base/lib/widgets/show-widgets.php, and added the following lines into the los_showPosts() function at the very top of its foreach($los_posts as $post) { loop:
$category = get_the_category($post->id);
if ($category[0]->slug == ‘sitedevelopmentblog’) continue;
