I want my "Contract Review" profile to be able to delete contacts as necessary from the contacts module.

Currently I have the Contacts Module set to Private

I have my Contract Review profile set to View, Read, Edit, Delete for the Contacts Permissions Module

I want the Contract Review profile to be able to delete any contact, whether assigned to them or not as the contact owner.. Therefore, I created a Sharing Rule under Data Sharing Settings inside Security and Control. That rule is below

The Rule is to Share Contacts from Roles and Subordinates of the VP (every profile is a subordinate of the VP, therefore this should include all contacts) and to Share those records to the Contract Review Profile. The Permission is set to Read/Write/Delete. This sharing rule allows for the Contract Review profile to read and write, but for some reason they cannot delete even though the permission is set to let them delete contacts.  Is there something else I must be missing that I need to change the setting on? Any suggestions? Thanks