OK, published_at
is not the right thing to use here, as you’ve found it can be set at any point before publishing by setting a past or future (scheduled) published_at date.
Instead, you should be able to use the {{is}}
helper to check the context, eg:
{{^is "preview"}}
<section class="post-full-comments">
<div id='discourse-comments'></div>
<script type="text/javascript">
...
</script>
</section>
{{/is}}