Post Visibility – Changing to Private makes it editable for Contributors

I’m creating a plugin to track Warranties using custom post types and I don’t want published posts to show up with Visibility: Public – but if I change the post status to Private, then users with Contributor status are then allowed to Edit the posts which are published, which I don’t want.

Looking for a solution to prevent Contributors from editing published, private posts…. or to just remove the text that displays the post Visibility status without removing the whole meta box. Just don’t want to spook Warranty owners from thinking their Warranty info is ‘Public’.