Trouble ordering posts in single.php

I am creating a template from scratch for the first time and am having issues getting single.php to follow the order of the referral page. For example, I have a page template that lists all posts in a specific order. Each list item links to the single post, from single.php I want to browse through the posts in the same order. This is what I have so far.

page-portfolio.php contains the following:

<?php
/*
 Template Name: Portfolio
 */
 get_header(); 

//SET QUERY ARGS, using custom post-type and order.
 $type = 'emid_portfolio';
 $args=array(
  'post_type' => $type,
  'orderby' => 'title',
  'order' => 'ASC',
  'post_status' => 'publish',
  'posts_per_page' => -1,
  'caller_get_posts'=> 1
);

//INIT QUERY
query_posts( $args );

//INIT LOOP
	if (have_posts()) :
		while (have_posts()) : the_post();

//OUTPUT LOOP CONTENTS
			echo='<a href="'.the_permalink().'">
						'.the_title().'
				</a>';
		endwhile; //have_posts() : the_post()
	endif; //have_posts()
wp_reset_query();
get_footer();

?>

and then single.php looks like this:

<?php

/**
 * The template for displaying all single posts.
 */

get_header(); ?>
	<div id="single" class="site-content">

		<?php
		if (have_posts()) :
			while (have_posts()) : the_post();
			?>
				<h3 class="float-left"><?php the_title() ?></h3>

					<div class="nav-single float-right">
						<?php
						previous_post_link('%link','<span class="port-nav prev"></span>');
						echo '<a href="'.get_site_url().'"><span class="port-nav main"></span></a>';
						next_post_link('%link','<span class="port-nav next"></span>');
						?>
					</div><!-- .nav-single -->
					<div class="clear"></div>

			<?php
			endwhile; // have_posts
		endif;
		?>
	</div><!-- #single -->

<?php get_footer(); ?>

I’ve tried creating a new WP_Query() as well as modifying the main query as done above with query_posts(). The page or category order changes but not the single.php order. I’ve also tried using:

//Modify Posts Order
function modify_query_order( $query ) {
    if( $query->is_main_query() ){
    	$query->set( 'orderby', 'title');
        $query->set( 'order', 'asc' );
    }
}
add_action( 'pre_get_posts', 'modify_query_order' );

in conjunction with archives.php. The order changes in the archives list but not in the menu when in single.php Any help would be greatly appreciated.

Thank you.