You can't find a box that UPS will ship and still honor their insurance. They want 4 in. of packing material all around the object. Anything but a small half A will end up too big to ship. Skip the packing and they won't honor the insurance, period.
Figure that at least one stage of your box's shipping experience there'll be some poor clunk who's standing at the intersection of a conveyor belt and a 30' trailer, with boxes coming off the conveyor at an average of once every five seconds or so. The only way to get the boxes to the end of the trailer when its empty is to pick one up, assess its weight, and if it is light enough hurl it the length of the trailer. Then when you get a heavy box you trot it to the end of the trailer, quickly arrange things, run back to the conveyor, and start hurling again.
(I have a cousin who worked at UPS until his back went out).
From their perspective, that 4" of packing is reasonable. I wouldn't use any less to ship by truck, either.
If you're not comfortable with tossing the box across ten feet of concrete floor, then you shouldn't be comfortable shipping it.