Sorry, no, it is not possible to remove the permalink slugs. They must exist. It is just how WordPress works. It needs the key/value pairs in order to function because this is how WordPress “know” how read the URL. So a category URL has to be:
directory.com/directory-home-page/cat/category-slug/
You can change the cat
part of the URL on the Connections Settings Advance admin page. But if you change it, it must be a value which does not conflict with WordPress or other custom post types (CPT) permalinks.
An individual entry permalink has to be this:
directory.com/directory-home-page/name/entry-slug/
You can change the cat
part of the URL on the Connections Settings Advance admin page. Again, if you change it, it must not conflict with other WordPress permalink slugs.
If you do not have the permalink slugs, WordPress will assume you are trying to load a blog post and thru a 404 not found error.