In general Content view restrictions add-on may help. It requires although that user with ‘ure_view_posts_access’ capability and permission to edit all those posts set manually, which roles are allowed to their content.

Take into account that, if user can edit the post, he automatically can view it.

You can not set view permission to the full post type at once currently. I think that it would enhance content view restrictions add-on usability and plan to add it to one of the future versions.