I usually recommend photo equipment shipping cases. Â Movie studios need to ship delicate cameras, lighting and other such elements all over the world. Â The cases are usually a sturdy black material with plenty of covering outside and (often) foam on the inside. Airlines are fairly familiar with them since they are pretty common with movie/tv shoots and such.
Due to the lack of cameras these days (film that is) most camera shops don't carry them anymore. Â But check online and you'll find several companies that offer them. Â And they come in just about every size you can imagine - 10x10x10, 12x12x12, 24x10x48, 48x48x48 and so on and so on. Â Some firms actually build costume boxes.
These were the boxes that Disneyland used back when I was there (1970s & 80s) and costumes were being shipped to events. Â They are the same boxes that a lot of the suits I wear on gigs today come in. Â This includes Astroboy, Tony the Tiger, Care Bears, etc. Â Only time I found a suit that did not was Boog the bear from OPEN SEASON. Â It was an enormous bell shaped body (perhaps 8 feet tall) that was shipped in a padded bag that my wife's car could have fit in! Â Sadly, each time we worked with the suit, we had to touch up the nose and other facial features due to scuffing and chipping during shipping.
Anyway, if I can locate the companies that sell the black camera cases, I'll put a link here. Â A buddy of mine bought one a year ago from a link I gave him and he says it is the best purchase he ever made for the suit.