Ammo must be three times contained;
The cartridge case of a loaded cartridge is considered the first containment.
Then box it or use the box's you bought them in.
Then place the box's of cartridges into a single box.
Then count them and label the package with type and amount of ammo, to and from info. Then seal the box.
Then go take it to your shipper, and let them slap the diamond and fill out the papers for cargo.
I use a 'common carrier" and there are cargo forwarders (Carlisle, here in Alaska) who will ship hazardous materials, aerosols and flammables.
They get stuff from the 48 to AK by plane or on a barge, then back to a plane, often.