In reply to Matt.

Untested, but probably can apply the principles from http://stackoverflow.com/questions/11124525/how-to-detect-custom-post-type-inside-admin-init-hook-callback

In short, need to check if the admin screen we're looking at is of the product post type, then fire off the filter that you want to use.

I haven't checked when the Pub filter fires to see if we can add it in that late or not.