I noticed previously that you specified initially that the packers are non-structural.
If you cannot extend the packer and add discrete fasteners to make it structural, use the second suggestion of my first post, and increase the total fastener strength by the amount of load which would be transferred in the case of a structural packer. That should cover the problem.
As an additional check, it would be wise to do a detail analysis of the fasteners, as there will be additional bending and prying, but adding capacity as described above should result in heavier and or stronger fasteners which can handle the extra eccentricity and resultant loads.
Hope this helps.
Regards,
Lcubed