Part of the trick is how it is packed. We went through this on our move from NY to Tx. There was a specialty packing company that came and had a whole selection of different foams-- with different "springiness" (what I referred to as durometer). They took measurements, evaluated the stuff to be crated- including the horns on my Avantgarde Duos. When they came back with the crates and packing, this was like custom level stuff. It was not cheap but everything they handled arrived unscathed.
So, in addition to freight brokers, etc. (I had a friend who palletized his cars to ship all over the world for events- back then it was "relatively" cheap), you gotta look at the packing. Once packed properly and palletized, you are pretty safe--
Never used craters and freighters- they aren't particularly cheap either. The company I used was a third party vendor to moving companies.
And obviously you aren't commissioning a flight just to take the Rhodes- it will tag a long with other stuff.
Good luck- I think some research here will pay off.