Move Thread Tags box above Quick Reply

For some reason on 4.x Internet Brands decided to move the Thread Tags box after Quick Reply. I have Similar Threads enabled, so thread tags are virtually hidden at the bottom of every page in showthread. The result is none of my members are using Thread Tags. I found the code for the tag box:

<vb:if condition="$show['tag_box']">
	<h4 class="threadinfohead blockhead">{vb:rawphrase tags_for_this_thread}</h4>
	<div id="thread_tags_list" class="thread_info_block blockbody formcontrols">
		<div class="inner_block">
			<vb:if condition="$show['manage_tag']">
			<a id="tag_edit_link" href="threadtag.php?{vb:raw session.sessionurl}t={vb:raw thread.threadid}" class="textcontrol" style="float:{vb:stylevar right}; font-size:11px; margin:10px;">{vb:rawphrase edit_tags}</a>
			</vb:if>
			<div id='tag_list_cell'>
				{vb:raw tag_list}
			</div>
			<p>
				<a href="tags.php{vb:raw session.sessionurl_q}">{vb:rawphrase view_tag_cloud}</a>
			</p>
		</div>
	</div>
	</vb:if>

Code (markup):

However when I move it from its default position, after:

{vb:raw similarthreads}
	{vb:raw template_hook.showthread_after_activeusers}

Code (markup):

I get this:


I can't figure out why it's showing the popupctrl dropdown and top button in the tag box header, and I can't seem to find the code in showthread that controls their placement. Ideally I'd like to have those two items display inline, to the left of the inline mod tools dropdown:



However if that's too complicated I'm willing to settle for having them not stuck inside the Tag Box header.

How do I do this?