How to create virtual pages with information from user meta profile fields?

Dave Jesch on his site presents a way to create virtual pages in WordPress. Dave created a class “to do all the heavy lifting“, as he says. I think, for my purposes this class not require changes, so I do not put it here. Also, Dave created a function (see bellow) that calls the above mentioned class to create a virtual page when is needed. I tested this method and it just works.

What I want, is to use the Dave’s class and function to put on my site a list of department members with links to their virtual pages with some content from their profiles. Pages must be virtual, so I do not have to create for each new member a real page, it must be created automatically (virtually) from his profile.

This is how I create and save some extra user profile fields:

/* Add Extra Fields to the User Profile */
add_action( 'show_user_profile', 'extra_user_profile_fields' );
add_action( 'edit_user_profile', 'extra_user_profile_fields' );

function extra_user_profile_fields( $user ) { ?>
   <h3><?php _e("Academic", "blank"); ?></h3>
   <table class="form-table">
      <!-- Teaching position -->
      <tr>
      <th><label for="teaching_position"><?php _e("Teaching position"); ?></label></th>
      <td>
      <input type="text" name="teaching_position" id="teaching_position" value="<?php echo esc_attr( get_the_author_meta( 'teaching_position', $user->ID ) ); ?>" class="regular-text" /><br />
      <span class="description"><?php _e("Put here your teaching position"); ?></span>
      </td>
      </tr>
   </table>
}

/* Save Extra User Profile Fields */
add_action( 'personal_options_update', 'save_extra_user_profile_fields' );
add_action( 'edit_user_profile_update', 'save_extra_user_profile_fields' );

function save_extra_user_profile_fields( $user_id ) {
   if ( !current_user_can( 'edit_user', $user_id ) ) { return false; }
   update_user_meta( $user_id, 'teaching_position', $_POST['teaching_position'] );
}

This is the Daves’s function that calls his class to create virtual pages:

function dj_create_virtual()
{
    $url = trim(parse_url($_SERVER['REQUEST_URI'], PHP_URL_PATH), '/');
    if ($url == 'dave-virtual-page') {
       $args = array('slug' => 'dave-virtual-page',
          'title' => 'Dave's Virtual Page',
          'content' => "This can be generated content, or static content<br />
          Whatever you put here will appear on your virtual page.");
       $pg = new DJVirtualPage($args);
    }
}
add_action('init', 'dj_create_virtual');

And this is how I display currently the members list of specific department on my site (with a shortcode):

add_shortcode( 'list_of_members', 'members_listing' );
/* usage: [list_of_members department = 'psychology'] */

function members_listing( $department ) {

   $members = get_users( array( 'meta_key' => 'department', 'meta_value' => $department ) ); 

   usort($members, create_function('$a, $b', 'return strnatcasecmp($a->last_name, $b->last_name);'));

   echo '<div id="memberlist"><ul>';
   foreach ( $members as $member ) {
      echo '<li>';
      echo get_avatar($member->ID);
      /* Bellow I want to put their names in a link to their virtual pages with some information from their profiles */
      echo '<div class="authname">' . $member->first_name . ' ' . $member->last_name;
      echo '</div></li>';
   }
   echo '</ul></div>';
}

Now I want, with the Dave’s class and function, to put in my (last) members_listing function the members names in links to their virtual pages with some information from their profiles. How to do this?

EDIT

Here are the functions in question as I have used them finally (many thanks to @g-m!):

function dj_create_virtual() {
   $url = trim( parse_url( $_SERVER['REQUEST_URI'], PHP_URL_PATH ), '/');
   if ( strpos( $url, 'users/' ) === 0 ) {
      $user_nicename = str_replace('users/', '', $url );
      $user = get_user_by( 'slug', $user_nicename );
      $user_info = array_map( function( $a ){ return $a[0]; }, get_user_meta( $user->ID ) );
      $args = array(
         'slug' => 'users/' . $user_nicename,
         'title' => $user_info['first_name'] . ' ' . $user_info['last_name'],
         'content' => get_avatar( $user->ID ));
      if( !empty( $user_info['teaching_position'] ) ) $args['content'] = $args['content'] . '<h5>Teaching position</h5>' . $user_info['teaching_position'];
      /* heare are some more user meta profile fields */
      $pg = new DJVirtualPage($args);
   }
}
add_action('init', 'dj_create_virtual');

and the members_listing function:

add_shortcode( 'list_of_members', 'members_listing' );
/* usage: [list_of_members department = 'psychology'] */

function members_listing( $department ) {
   $members = get_users( array( 'meta_key' => 'department', 'meta_value' => $department ) ); 
   usort( $members, create_function( '$a, $b', 'return strnatcasecmp($a->last_name, $b->last_name);' ) );
   echo '<div id="memberlist"><ul>';
   foreach ( $members as $member ) {
      echo '<li>';
      printf( '<div class="authname"><a href="%s">%s</a>', home_url( '/users/' . $member->user_nicename ), get_avatar( $member->ID ) );
      printf( '<div class="authname"><a href="%s">%s</a>', home_url( '/users/' . $member->user_nicename ), $member->display_name );
      if( !empty( $member->teaching_position ) ) { echo '<br />' . mb_convert_case( $member->teaching_position, MB_CASE_LOWER, 'UTF-8' ); };
      echo '</div></li>';
   }
   echo '</ul></div>';
}