One of the problems with large organizations of any sort is their compartmentalization, and the failure of the various component part to communicate with one another.
Rather than organizing public input around specific departments, agencies, and bureaus, why not organize it around the issues that effect each. In this way, no matter what government department, agency, or bureau a government employee might work for, he or she could sign on to the issue or issues that is of concern to him or her. At times a particular department, agency, bureau, or other body of government might itself become an issue. No harm done.
Organizing the issues could easily be achieved through statistical clustering, and everyone -- both the general public and the government -- could find the issue of particular interest to him or her through key word searches.