I think I have figured this out, and decided to post my solution in case anyone in the future would like to do something similar.
This is all done via a custom functions.php file in a child theme directory. No need to touch any of the default thematic files.
Let's assume one wants the following output in the header:
<div id="header">
<div id="bloginfo">
<h1 id="blog-title"></div>
<div id="blog-description"></div>
</div><!--#bloginfo-->
<div id="search"></div>
<div id="navigation"></div>
</div><!--#header-->
First, you need to remove some of the default output by putting the following into your functions.php file:
// Take Away Default Thematic Header
function new_header() {
remove_action('thematic_header','thematic_brandingopen',1);
remove_action('thematic_header','thematic_blogtitle',3);
remove_action('thematic_header','thematic_blogdescription',5);
remove_action('thematic_header','thematic_brandingclose',7);
remove_action('thematic_header','thematic_access',9);
}
add_action('init', 'new_header');
Now that you have removed some of the default output, you can add your own custom output by doing the following:
// Insert Custom Header
function custom_header() { ?>
<div id="bloginfo">
<h1 id="blog-title"></h1>
<div id="blog-description"></div>
</div><!-- #bloginfo -->
<div id="navigation"></div>
<?php }
add_action('thematic_header','custom_header');
That should do the trick.