I figured it out on my own. If anyone is interested, here is a sample of the solution.
At the top of my template, before any loops, I have the following code to check to see what category the page I am on is and return its ID.
<?php foreach(get_the_category() as $category)
{ $thecat = $category->cat_ID; } ?>
Then, at the start of each loop I have the following. This code is set to call specific, constant post tags in respect to the particular category archive I am on.
<h2>30 Sheets</h2>
<?php query_posts('cat=' . $thecat . '&tag=30-sheets&order=ASC'); ?>
<?php if (have_posts()) : ?>
<?php while (have_posts()) : the_post(); ?>
---- THE CONTENT YOU WANT TO SHOW GOES HERE ----
<?php endwhile; ?>
<?php else : ?>
<div id="page">
<p class="center">There are no records for this media.</p>
</div>
<?php endif; ?>
<h2>Mall Kiosks</h2>
<?php query_posts('cat=' . $thecat . '&tag=mall-kiosks&order=ASC'); ?>
<?php if (have_posts()) : ?>
<?php while (have_posts()) : the_post(); ?>
---- THE CONTENT YOU WANT TO SHOW GOES HERE ----
<?php endwhile; ?>
<?php else : ?>
<div id="page">
<p class="center">There are no records for this media.</p>
</div>
<?php endif; ?>
You can do this for as many loops and tags as you like.