override teaser in story template (or blog etc) does not control certain variables?

Contemplate was not written to remove the items you are looking at, it is specifically written to manage the content in the node wrappers, i.e.: teaser, body, RSS item. I don't know of a way to remove these things using Contemplate.

I would change the Theme.

For example, Drupal 6.1 using the Garland theme: This is themes/garland/node.tpl.php

<?php
// $Id: node.tpl.php,v 1.5 2007/10/11 09:51:29 goba Exp $
?>
<div id="node-<?php print $node->nid; ?>" class="node<?php if ($sticky) { print ' sticky'; } ?><?php if (!$status) { print ' node-unpublished'; } ?>">
<?php print $picture ?>

<?php if ($page == 0): ?>
  <h2><a href="<?php print $node_url ?>" title="<?php print $title ?>"><?php print $title ?></a></h2>
<?php endif; ?>

  <?php if ($submitted): ?>
    <span class="submitted"><?php print $submitted; ?></span>
  <?php endif; ?>

  <div class="content clear-block">
    <?php print $content ?>
  </div>

  <div class="clear-block">
    <div class="meta">
    <?php if ($taxonomy && ($node->type != 'story')): ?>
      <div class="terms"><?php print $terms; ?></div>
    <?php endif;?> 
    </div>

    <?php if ($links): ?>
      <div class="links"><?php print $links; ?></div>
    <?php endif; ?>
  </div>
</div>

The above is an example of a node.tpl.php file, notice the section:

  <?php if ($taxonomy && ($node->type != 'story')): ?>
      <div class="terms"><?php print $terms; ?></div>
  <?php endif;?> 

Originally it was:

  <?php if ($taxonomy): ?>
      <div class="terms"><?php print $terms; ?></div>
  <?php endif;?> 

You would need to make a custom theme by editing the template files *.tpl.php.