Here's what you might be able to do. First create a theme template file for each category. Make sure that each category template's file name is category-x.php, where x is the id number of that category. Create category-x.php with all the important template tags and your theme code. Right below the template tag (or wherever you want honestly) for the content in each template, put wp_list_pages with the child_of condition like so..
<?php wp_list_pages('child_of=x'); ?> <--x is the id of the correct parent page.
I'm guessing that wp_list_pages would need to be outside of the loop.
Second create a page corresponding to each of the categories you have. These parent pages will be sort of surrogate categories for your pages.
If you take all that work once, you'll have the normal page that holds all the posts in one category with a list of pages in the same sort of category.
Does that make any sense? I haven't tried this but I'm pretty sure it'd work.