My friends who have shipped guns from europe to the US have had to have their FFL go in person to the airport and pick up the guns. What paperwork was required also varied by who was working at Customs. Sometimes we had to have them get out the manual and point out to them that we did have the correct paperwork. Even after this he said he had to talk to a supervisor and made us come back the next day. Talk to several people at ATF and Customs. After you get answers contact different people at each agency and get their answers and see if they mesh. Importing a gun is not as straightforward as it might be, but it is possible to do on your own with the assistance of a local FFL.
Regards,
Jeff

"We are men of action. Lies do not become us."
Wesley