I would really suggest using one custom post type and one custom taxonomy with terms under the custom taxonomy which is assigned to a show.
This structure will function exactly like normal posts with normal categories, the only difference is that it will be outside the scope of default blogging as custom post types are excluded from the main query.
There are methods and plugins to change the post type of a post. I would recommend to create one custom post type, then change all the tv shows custom post types to this custom post type and then delete all the other custom post types
You can now create a taxonomy for this custom post type. This will add a metabox to the custom post type post screen which operates the same as that for normal categories. You can go to the custom taxonomy screen and create terms (like categories) which you can assign to a post the same way as you would do it for normal posts and categories
Just one tip, test this locally and play around with it before applying it to a live site, and always create a backup before making changes