Next/previous post link to posts only within one or more specific categories

I solved it by abandoning the code and registering a new taxonomy. I then used this code in single.php:

<?php if (has_term('[TERM-NAME]', '[TAXONOMY-NAME]')) : ?>
        <div class = "next-post"><?php next_post_link('%link &raquo;', '%title', true, '', '[TAXONOMY-NAME]') ?></div>
        <div class = "prev-post"><?php previous_post_link('&laquo; %link', '%title', true, '', '[TAXONOMY-NAME') ?></div>
<?php endif; ?>

Doing it like this allows me to have multiple categories since I only assign one term in the custom taxonomy per post.