I do a lot of shipping of high dollar merchandise.
Advice... when you pack a barrel or an upper, tape some heavy cardboard over the ends. Then wrap the whole thing in several layers of bubble wrap, paying attention to wrap around each end. You want at least 2" of thickness of bubble wrap, 3" is better. On the each end you want no less than 3" of bubble wrap.
If the pkg is dropped on its side, it is not likely that there will be any damage as the force will be spread over the whole side of the barrel or upper half.
BUT when the pkg is dropped on end, that force is concentrated on the very small muzzle, or the chamber end of the barrel, or back end of the receiver. This can punch through wrapping and damage the item you are shipping.
Also, you don't want a hole punched in the end, things hanging out, people seeing what is in the box. So pay a lot of attention to padding the ends.
Do not use a box with gun company logos. The contents are to be described as "machine parts".
Addressing: You do not want to use a shipping address like "Johnny's Gun Shop", etc. For companies like J&T, ADCO, etc, those names are pretty innocuous. So, call "Johnny's" and ask if you can ship to JGS, Inc or whatever alternate name he uses. Many gun businesses work this way, it reduces the theft problem.