Get a List of All Commenters on the Current Post

I'm trying to get a list of everyone who's commented on a post, and then check that list against the current logged in user. If the current logged in user is included in that list, then I don't show the comment form, otherwise they can leave a comment. So essentially, I only want people to be able to comment once per post.

I think I'm close, but I keep pulling in a list of everyone who's commented on any post.

Here's my code:

    <?php global $post;
      $comments = get_comments($post->ID); // get all comment author emails
      foreach($comments as $comment) :
        $existingcommenters = $existingcommenters.', '.$comment->comment_author_email;
      endforeach;

      $current_user = wp_get_current_user(); // then we check those emails against the current users email
      $commenting = $current_user->user_email; ?>

<?php $args = array( // i then list my arguments, which I've omitted for clarity here
    ); ?>

<?php if (strpos($existingcommenters,$commenting) !== false) { // if the user already has a review, don't let them post another ?>
    <p>You've already reviewed this business.</p>
<?php } else { comment_form($args); } ?>

So I thought $existingcommenters should only contain a list of people who've commented on this post, as $comments = get_comments($post->ID); should be setting that call to only get a list of comments for this post, right?

If I echo $post->ID anywhere in this code, it does return the current post's ID successfully.

But if I echo $existingcommenters, it shows a list of every single commenter.

Any idea what I might be doing wrong?