I would like the HQ Forest to be able to see all Branch Partner publications even if not included in the Specify Permissions screen when creating a new publication and everyone permission is removed.
If the Everyone permission is removed and the HQ is not added to the list of Partners as Allow when creating the publication, then the HQ will not see the publication. This also applies to all other collaboration partners. If the Everyone permission is removed, you need to manually add (Allow) those partners who you would like to subscribe to your publication, including the HQ Forest. Deny will always override an Allow.
Enhancement Request TF00222244 has been submitted to Development for possible consideration in a new release of Collaboration Services.