Need help rethinking Runway collection "related items" code

One of my sites is experiencing much higher traffic than normal today (1,000+ concurrent users -- "normal" is 5). When the spike started, load time for the page in demand went from 1s to 40s until I removed a bit of code from my Runway page template, at which point load time dropped right back down to 1s.

The bit of code I removed searches through all collection items (currently 1,200 items) to find other items with the same categories as the item being viewed. Basically I'm just putting all of the categories for the current item into an array to be used with the category option for perch_collection() which retrieves the related posts. Here's the page template:

$result = perch_collection('Blog Posts',array(
  'template' => 'blog/posts/_post.html',
  'filter'=>'postSlug',
  'match'=>'eq',
  'value'=>perch_get('post'),
  'skip-template' => true,
  'return-html' => true,
  'count' => 1,
));

perch_layout('global/header',[
  'blog-post' => true
]);

echo $result['html'];

// related posts
$cats = perch_collection('Blog Posts',array(
  'template' => 'blog/_get_cat_array.html',
  'filter'=>'postSlug',
  'match'=>'eq',
  'value'=>perch_get('post')
),true);
$cats = explode(",",$cats);
perch_collection('Blog Posts',array(
  'template' => 'blog/posts/_related_posts.html',
  'count'=>3,
  'sort'=>'postDateTime',
  'sort-order'=>'RAND',
  'category'=>$cats,
  'filter'=>[
    [
      'filter'=>'postSlug',
      'match'=>'neq',
      'value'=>perch_get('post')
    ],
    [
      'filter'=>'postDateTime',
      'match'=>'lte',
      'value'=>date('Y-m-d H:i:s')
    ]
  ],
));

perch_layout('global/footer',[
  'scripts'=>'<script type="text/javascript" src="/js/rrssb.min.js?v=2018021201"></script>'
]);

...

This is the part of that code that was causing high load:

// related posts
$cats = perch_collection('Blog Posts',array(
  'template' => 'blog/_get_cat_array.html',
  'filter'=>'postSlug',
  'match'=>'eq',
  'value'=>perch_get('post')
),true);
$cats = explode(",",$cats);
perch_collection('Blog Posts',array(
  'template' => 'blog/posts/_related_posts.html',
  'count'=>3,
  'sort'=>'postDateTime',
  'sort-order'=>'RAND',
  'category'=>$cats,
  'filter'=>[
    [
      'filter'=>'postSlug',
      'match'=>'neq',
      'value'=>perch_get('post')
    ],
    [
      'filter'=>'postDateTime',
      'match'=>'lte',
      'value'=>date('Y-m-d H:i:s')
    ]
  ],
));

...

This is _get_cat_array.html:

<perch:categories id="categories" set="blog" >blog/<perch:category id="catSlug" type="slug" /><perch:if not-exists="perch_item_last">,</perch:if></perch:categories>

...

Is there some better way of doing this which won't cause so many round trips to the db? Thanks for the help!