Mind you I do fly internationally into the US, but we HAVE to have the ammo and gun in separate bags. I ship our ammo down well in advance when we cross into NY on our way to a match and hit up a UPS center on a Friday afternoon. I've never had an issue contacting whoever is running the match and shipping the ammo down to an address they've given me. It's been 2/3's to their home the time other to the range.
UPS isn't consistent but I did have to provide ID the first time this year along with a question "Cartridges" ? The other time the guy was too busy staring at my wife's bosom to care about anything. I also managed to get a US based UPS account so I don't have to pay retail like last year. I ship a decent amount for a small biz.
I do use the plastic boxes. I also bought the nylon reinforced packing tape. I usually tape 3 boxes together wrapping around all 4 sides. The cardboard box can't be too big and I usually double box and then wrap it in brown paper completely covered in clear packing tape. With the ORM-D printed on orange paper. Never had a issue. Getting the nylon tape off can be a bit of a pain.
The ammo boxes are breaking as they are shifting around during transport. Pack that sh*t tight!! You should see the conveyor systems the big companies use, it's not delicate by any means.