Thank you very much for your swift response Angelo.
The post you pointed me to, was exactly what I was looking for!
Suppose stepping out of my comfort zone and diving into the template structure is the best way to achieve true integration.
To get it working I first had to turn off formatting for events categories.
The code above is from my theme category.php template. I copied that template to my child theme and renamed it to taxonomy-event-categories.php, as the plugin author suggests here:
https://www.ads-software.com/support/topic/plugin-events-manager-single-category-template
I then replaced the above code snippet with this:
<div class="col-sm-8 col-md-9">
<?php
global $post, $EM_Category, $wp_query;
$EM_Cat = em_get_category($wp_query->queried_object->term_id); ?>
<?php echo $EM_Cat->output('#_CATEGORYNEXTEVENTS'); ?>
</div>
<div class="col-sm-4 col-md-3 sidebar">
<?php get_template_part('templates/sidebar') ?>
</div>
Once again, thank you so much for your help Angelo.