A suggestion for shipping barrels - especially long barrels:
Shippers hate long items and round tubes in general. They tend to fall off the conveyers and have to be hand carried to their next point. And agree, damage will usually occur at the distribution centers. The heavy wall cardboard tubes are probably OK for barrels about 36" or shorter. Here is how I ship a barrel to be worked on:
Go to Lowe's or Home Depot and have them cut you an appropriate length of schedule-40 PVC pipe. Probably 2" in diameter. But measure around the widest point of the barrel to take into consideration for any sights, thimbles, etc. Might have to use 2.5" or 3" diameter in some cases. Then, purchase two matching female threaded ends and PVC glue them to both ends. Then thread PVC caps to both ends (not glued so the tube can be opened and inspected if necessary). While you're at the store, purchase a length of Air Conditioning foam line insulation to easily wrap the barrel with and slide into the PVC tube.
The PVC tube will add weight. Thus, more shipping cost. But it's virtually guaranteed to get there and back to you in one piece. Plus, it allows the gunsmith to easily unpack the barrel and re-pack the same way. Just slap a new label on it.