I went ahead and removed the table since I couldn't get some parts of the border to go away and I got it looking good enough anyways with a couple quick alterations to the code, as seen below:
<div class="navigation" style="padding-top: 15px; padding-bottom: 10px;">
<div style="float: left;"><?php previous_post_link('« %link') ?></div>
<div style="float: right;"><?php next_post_link('%link »') ?></div>
</div>
I ended up putting this at the top of the post and at the bottom as well, above the comments.
Here's the end result: http://kurtiskronk.com/2008/12/16/standing-in-wait/
And for reference, for anyone else looking to do the same thing, here are the entire contents of my single_default.php for the Carrington theme:
<?php
// This file is part of the Carrington Theme for WordPress
// http://carringtontheme.com
//
// Copyright (c) 2008 Crowd Favorite, Ltd. All rights reserved.
// http://crowdfavorite.com
//
// Released under the GPL license
// http://www.opensource.org/licenses/gpl-license.php
//
// **********************************************************************
// This program is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
// **********************************************************************
if (__FILE__ == $_SERVER['SCRIPT_FILENAME']) { die(); }
if (CFCT_DEBUG) { cfct_banner(__FILE__); }
get_header();
?>
<div id="content">
<div class="navigation" style="padding-top: 15px; padding-bottom: 10px;">
<div style="float: left;"><?php previous_post_link('« %link') ?></div>
<div style="float: right;"><?php next_post_link('%link »') ?></div>
</div>
<?php
cfct_content();
?>
<div class="navigation" style="padding-top: 15px; padding-bottom: 10px;">
<div style="float: left;"><?php previous_post_link('« %link') ?></div>
<div style="float: right;"><?php next_post_link('%link »') ?></div>
</div>
<div id="comments">
<?php
comments_template()
?>
</div><!--#comments-->
</div><!--#content-->
<?php
get_sidebar();
get_footer();
?>
Many thanks to figaro, jabecker, and dgold for help doing this. Ended up being more simple than I realized, but the fact that this theme's code was so different from my other themes confused me thoroughly. :-D