previous/next_post_link() ordered by custom

I’m developing a business directory with WordPress. The “members” category is ordered by the “city” custom value. I have a nice query that makes this happen (based on a codex query):

<?php

 $querystr = "
SELECT * FROM $wpdb->posts
LEFT JOIN $wpdb->postmeta ON($wpdb->posts.ID = $wpdb->postmeta.post_id)
LEFT JOIN $wpdb->term_relationships ON($wpdb->posts.ID = $wpdb->term_relationships.object_id)
LEFT JOIN $wpdb->term_taxonomy ON($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id)
WHERE $wpdb->term_taxonomy.term_id = 3
AND $wpdb->term_taxonomy.taxonomy = 'category'
AND $wpdb->posts.post_status = 'publish'
AND $wpdb->postmeta.meta_key = 'city'
ORDER BY $wpdb->postmeta.meta_value ASC
";

 $posts = $wpdb->get_results($querystr, OBJECT);
 ?>

All works very well until I get to the single.php template for this category. Here, the navigation previous_post_link() and next_post_link() functions are not jiving with the custom order in the category.php template.

How can I create a custom query that changes the order of the prev/next post links based on the query above for my single.php template?