I'm not a big fan of how WP has implemented menus... it's pretty idiotic, so forgive my blatant dislike of it.
The thing is that the "default" WP menus only support "cherry-picking": i.e. you pick which posts or pages you want. Basically, you get some eye-candy that achieves the same thing as pasting some raw HTML into your theme files = epic fail in my opinion.
The gold you're after is *dynamic* menus, and that's NOT something WP shines at. You have to do so indirectly by using Categories: put your custom posts into a category, and add that category to the menu. (Enable categories on your custom post-type under the "Taxonomy" tab when you create or edit your custom content type definition). You'll notice that this approach gives you no control over order of the menu items.
The other approach I would recommend is not one that WP would approve of, but given WP's disastrous architectural decisions, that may not be a bad thing. Here's the alternative approach:
1. Create a WP page dedicated to displaying a list of your custom posts. Since it's a page, you can select a dedicated template file to format it.
2. On that page's template, use PHP to select and display your custom posts (e.g. using get_posts() or my other plugin: Summarize Posts).
By using a raw PHP function to select your posts, you can ensure that you select the posts you want and that you format and order them the way you want. You can put this same type of PHP code into your header.php file to dictate how those posts display.
Hope that makes sense. WP is very poorly structured in this regard, so you have dig your way out of the mess it created. Note that this isn't at all related to the CCTM plugin: you have the same hurdles when adding regular posts and pages to your site.