Custom topic tags, please point me in the right direction!

For the first one, the function you will want to look at is qpservices_amplify_propernouns(). You can just edit the $out variable, which formats the output of that block.

For the second one, there is currently no way of blacklisting. One way of doing this would be to change this:

function qpservices_amplify_propernouns() {
  if (arg(0) == 'node' && ctype_digit(arg(1))) {
    $node = node_load(arg(1));
    $qp = amplify_get_qp($node);
    if (empty($qp)) {
      return '';
    }
    
    $qp->find('ProperNouns>TopicResult>Topic>Name')->slice(0, 20);
    
    $out = qp('<?xml version="1.0"? ><ul/>');
    $temp = '<li><a href="%s">%s</a></li>';
    foreach ($qp as $name) {
      $out->append(sprintf($temp, '#', $name->text()));
    }
    return $out->top()->find('ul')->xml();
  }
}

To something like this:

function qpservices_amplify_propernouns() {
  if (arg(0) == 'node' && ctype_digit(arg(1))) {
    $node = node_load(arg(1));
    $qp = amplify_get_qp($node);
    if (empty($qp)) {
      return '';
    }
    
    $qp->find('ProperNouns>TopicResult>Topic>Name');

    $stopwords = array ('words', 'I', 'do', 'not', 'want');

    $ok_words = array();
    foreach ($qp->find('ProperNouns>TopicResult>Topic>Name') as $word) {
      $word_text = $word->text(); // $word is really a QueryPath object, so we get the text with text()

      if (!in_array($word_text, $stopwords)) {
        $ok_words[] = $word_text;
      }
    }

    $out = qp('<?xml version="1.0"? ><ul/>');
    $temp = '<li><a href="%s">%s</a></li>';
    foreach ($ok_words as $name) {
      $out->append(sprintf($temp, '#', $name));
    }
    return $out->top()->find('ul')->xml();
  }
}