As far as i know, no current CMS/Blog system can do what you're asking, you're gonna have to either link to something or link to it through an iframe like I suggested, or make your own theme.
Your site doesn't look that complex, if you really want a blog, you might as well just turn your site into a wordpress theme as there isn't really anything super fancy involved, its really more a matter of just adding some of the template tags I linked to and possibly some page re-structuring.
Now I haven't tried this as I've built my stuff from scratch with the intention of making a theme but this should more or less work
1. Assuming you have wordpress installed, go to wp-content/themes/
2. Add a folder that will hold your theme/site. Move all your files to that folder
3. Rename your blog page to "single.php" and add this to where you want the blog to show up
Code:
<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
<?php the_content();?>
<?php endwhile; else: ?>
<p><?php _e('Sorry, no posts matched your criteria.'); ?></p>
<?php endif; ?>
4. Activate theme in dashboard.
Again, I haven't tried this, but this should bring up all the posts you make on Wordpress on the blog page.
I almost forgot, you'll have to add this to your stylesheet, of course, replacing the information with your own. Otherwise Wordpress won't be able to see your site.
Code:
/*
Theme Name: Rose
Theme URI: the-theme's-homepage
Description: a-brief-description
Author: your-name
Author URI: your-URI
Template: use-this-to-define-a-parent-theme--optional
Version: a-number--optional
.
General comments/License Statement if any.
.
*/