Overriding comment admin overview output [SOLVED]

I'm working on a custom module to help out the moderators on my website by adding additional functionality, and one of these is simply adding a "Check IP" column with the comment's hostname on each field on the Comment Approval page. In addition, I will also be needing a way to alter the query to join the Comments table with my module's table later on, but that's not the concern for now.

Anyway, I can accomplish all of the above by making the following alterations to these two functions in the comment.admin.inc file in the core's Comment module...

function comment_admin_overview($type = 'new', $arg) {
  // build an 'Update options' form
  $form['options'] = array(
    '#type' => 'fieldset', '#title' => t('Update options'),
    '#prefix' => '<div class="container-inline">', '#suffix' => '</div>'
  );
  $options = array();
  foreach (comment_operations($arg == 'approval' ? 'publish' : 'unpublish') as $key => $value) {
    $options[$key] = $value[0];
  }
  $form['options']['operation'] = array('#type' => 'select', '#options' => $options, '#default_value' => 'publish');
  $form['options']['submit'] = array('#type' => 'submit', '#value' => t('Update'));

  // load the comments that we want to display
  $status = ($arg == 'approval') ? COMMENT_NOT_PUBLISHED : COMMENT_PUBLISHED;
  $form['header'] = array('#type' => 'value', '#value' => array(
    theme('table_select_header_cell'),
    array('data' => t('Subject'), 'field' => 'subject'),
    array('data' => t('Author'), 'field' => 'name'),
    array('data' => t('Hostname'), 'field' => 'hostname'),
    array('data' => t('Posted in'), 'field' => 'node_title'),
    array('data' => t('Time'), 'field' => 'timestamp', 'sort' => 'desc'),
    array('data' => t('Operations'))
  ));
  $result = pager_query('SELECT c.subject, c.nid, c.cid, c.comment, c.hostname, c.timestamp, c.status, c.name, c.homepage, u.name AS registered_name, u.uid, n.title as node_title FROM {comments} c INNER JOIN {users} u ON u.uid = c.uid INNER JOIN {node} n ON n.nid = c.nid WHERE c.status = %d'. tablesort_sql($form['header']['#value']), 50, 0, NULL, $status);

  // build a table listing the appropriate comments
  $destination = drupal_get_destination();
  while ($comment = db_fetch_object($result)) {
    $comments[$comment->cid] = '';
    $comment->name = $comment->uid ? $comment->registered_name : $comment->name;
    $form['subject'][$comment->cid] = array('#value' => l($comment->subject, 'node/'. $comment->nid, array('attributes' => array('title' => truncate_utf8($comment->comment, 128)), 'fragment' => 'comment-'. $comment->cid)));
    $form['username'][$comment->cid] = array('#value' => theme('username', $comment));
    $form['hostname'][$comment->cid] = array('#value' => l($comment->hostname, 'http://whatismyipaddress.com/ip/'. $comment->hostname));
    $form['node_title'][$comment->cid] = array('#value' => l($comment->node_title, 'node/'. $comment->nid));
    $form['timestamp'][$comment->cid] = array('#value' => format_date($comment->timestamp, 'small'));
    $form['operations'][$comment->cid] = array('#value' => l(t('edit'), 'comment/edit/'. $comment->cid, array('query' => $destination)));
  }
  $form['comments'] = array('#type' => 'checkboxes', '#options' => isset($comments) ? $comments: array());
  $form['pager'] = array('#value' => theme('pager', NULL, 50, 0));
  return $form;
}

function theme_comment_admin_overview($form) {
  $output = drupal_render($form['options']);
  if (isset($form['subject']) && is_array($form['subject'])) {
    foreach (element_children($form['subject']) as $key) {
      $row = array();
      $row[] = drupal_render($form['comments'][$key]);
      $row[] = drupal_render($form['subject'][$key]);
      $row[] = drupal_render($form['username'][$key]);
      $row[] = drupal_render($form['hostname'][$key]);
      $row[] = drupal_render($form['node_title'][$key]);
      $row[] = drupal_render($form['timestamp'][$key]);
      $row[] = drupal_render($form['operations'][$key]);
      $rows[] = $row;
    }
  }
  else {
    $rows[] = array(array('data' => t('No comments available.'), 'colspan' => '6'));
  }

  $output .= theme('table', $form['header']['#value'], $rows);
  if ($form['pager']['#value']) {
    $output .= drupal_render($form['pager']);
  }

  $output .= drupal_render($form);

  return $output;
}

Works perfectly, and I can even alter the sql query for the results and join my custom module's database with the comments later on. One flaw in this as any Drupal developer will immediately point out: "Hacking core is bad, mmmkay." So I copied the above code out of the core module and into my custom module, figuring I could override these two core functions with a "hook."

However, it is not working. Tried "mymodule_comment_admin_overview," "mymodule_preprocess_comment_admin_overview," and other combinations along with clearing the cache each time, but my custom module will not override core's output. Haven't tried it in the theme's template.php file, but I would really rather keep this in a custom module and out of the theme (easily reusable on other sites). What am I doing wrong?