I ship quite a few guns and have had good luck with the method I have developed. I break down the gun and put the 4end back on the barrels. I have had felt sleeves made for the 2 halves . Each half goes in a felt sleeve and is wrapped with stretch wrap. Then each half is wrapped in foam padding and secured with stretch wrap. Then the two half are secured together with stretch wrap. This is the placed in a 6x6x36 double wall carton with bubble wrap to take up any remaining space. The result is 2 parts enclosed securely that cant move or come in contact with each other inside a rigid carton that does not look like a gun.
I don't want the carriers to take this as a challenge but so far this has worked with lots of guns getting to the destination without damage. The moral of the story is over packing is your best insurance.
Hammerguns need special attention to ensure the hammers are protected .
I used to use Plano take down cases inside a carton and had good luck with them as well but the expense and space they take up got to be too much