Processed is easy, it is cleaned and packaged as if it were from the store - i.e. fully dressed, cleaned, and packaged. This isn't an option for most as it is necessary to leave a fully feathered wing and/or foot for identification. If the birds were processed by a commercial operator they might be importable but there are then import fees that may apply. This is actually similar to transporting venison from chronic wasting disease areas.
A VS (vetinary services) permit is typically issued for animals being transported into the U.S. I've known of these to be issued for live research animals and had an acquaintance get one (in addition to a CITES permit at the time) to ship a crane to a taxidermist as he wasn't going straight home from that hunt. Whether it can be used for transport of dead meat I don't know.
I'm guessing a USDA approved establishment might be a licensed meat processor or holding facility where the animal(s) could be quarantined or tested for specific disease. I think this is what is done when animals are brought into Hawaii.
