How does one add a Total(s) row to Views results?
I'd like to make the Total row part of the table, rather than a hacky
solution where I calculate it in the view header or footer. How can
this be done?

I've never used that module, but alternatively, you could do the template file solution.
Since you want this to work in the View's preview, which uses core's admin theme and since you should never hack core, this cannot be solved via theme. Therefore, must be solved via custom module.
Example:

View ID: content
View Display ID: page_1

/mymodule/mymodule.module
/*
 * Implements template_preprocess_views_view_table()
 */
function mymodule_preprocess_views_view_table(&amp;$variables) {
  $view = $variables['view'];
  if ($view-&gt;id() == 'content' &amp;&amp; $view-&gt;current_display == 'page_1') {
    $variables['total_rows'] = $view-&gt;total_rows; // pass custom var to template
  }
}

/*
 * Implements hook_theme()
 */
function mymodule_theme() {
  return array(
    'views_view_table__content__page_1' =&gt; [
      'template' =&gt; 'views-view-table--content--page-1',
      'base hook' =&gt; 'view',
    ],
  );
}

/mymodule/templates/views-view-table--content--page-1.html.twig
Copy the code of views-view-table.html.twig and paste into this file and just change the last 3 lines to:
  {% endfor %}
  &lt;tr&gt;
    &lt;td&gt;{{ 'Total'|t ~ ' | ' ~ total_rows }}&lt;/td&gt;
  &lt;/tr&gt;
  &lt;/tbody&gt;
&lt;/table&gt;