You can try to use the `the_post` filter, to override the content pagination, that takes place within the `setup_postdata()` function ( *PHP 5.4+* ):

    /**
     * Ignore the <!--nextpage--> for content pagination.
     * 
     * @see http://wordpress.stackexchange.com/a/183587/26350
     */

    add_action( 'the_post', function( $post )
    {
    	if ( false !== strpos( $post->post_content, '<!--nextpage-->' ) ) 
    	{
            // Reset the global $pages:
    		$GLOBALS['pages']     = [ $post->post_content ];
            
            // Reset the global $numpages:
            $GLOBALS['numpages']  = 0;

           // Reset the global $multipage:
            $GLOBALS['multipage'] = false;
    	}
    	
    }, 99 );
    
to ignore the `<!--nextpage-->` feature. 

The global `$pages` variable contains the paginated content:

    $pages = explode('<!--nextpage-->', $content);

so that's why we need to restore it to:

    $pages = array( $post->post_content );

We actually don't need to restore the `$numpages` variable, but we do it as part of the house cleaning. If we only restored `$pages` and `$numpages=0` then we would get: 

    <div class="page-links">Pages:</div>	

The `wp_link_pages()` function [checks][1] if the global `$multipage` is true to display the content pagination output. So that's the variable to set to false to remove the whole output. We could also use the `wp_link_pages` filter to remove it.


  [1]: https://core.trac.wordpress.org/browser/tags/4.1.1/src/wp-includes/post-template.php#L779