Remove CPT Slug

There is now an easy solution to this thankfully. You can find the full solution here:
https://raisor.io/how-to-remove-the-post-type-cpt-slug-from-custom-post-type-permalink/

To summarize

1. Install the Custom Post Type Permalinks plugin and the Remove CPT base plugin
2. Set your CPT permalinks on the Permalinks settings page
3. Go to Settings > Remove CPT base and check the boxed for the post types you want to remove the CPT slug from