Use different comment template for replies-to-top-comment
I manage to solve this problem by exploiting the pid (parent ID) value in the $comment variable. First, I check if the corresponding comment is a top-level comment. It is a top level comment if the pid value is 0. The code inside comment.tpl.php so far is:

if ($comment-&gt;pid == 0) {
  // Top level comments code here
} else {
  // Replies to comments code here
}


The code above will split the template programatically already, but it will be better if I worked at two separate files for the two cases. To do this, I used drupal_get_path function to point every case inside comment.tpl.php to their corresponding template.

In my case, I create these two templates inside my theme folder:


/templates/comment/comment-top.tpl.php for the top comment
/templates/comment/comment-reply.tpl.php for the replies


The code inside comment.tpl.php then become:

if ($comment-&gt;pid == 0) {
  include drupal_get_path('theme', 'mytheme') .
    '/templates/comment/comment-top.tpl.php';
} else {
  include drupal_get_path('theme', 'mytheme') .
    '/templates/comment/comment-reply.tpl.php';
}


Of course change the mytheme in the code to your theme name.

To finish off, I pasted the template I posted above in the question to the corresponding template. It will render the template properly with all the variables you define inside the preprocesses function working.