Have you looked at pallet carriers? More expensive I bet; and you'd need to build a wooden box to ship it in. I guess a bonnet is a full pallet if its flat but with the right box it could be sent upright and might then sneak in as half a pallet.
I used to work for a removals company. On occasion, when we took people abroad, we would carry extra bits for people if we had space.
Bit of a long shot, but maybe worth calling a few of the removers that do overseas stuff and asking them?