Call one of the large taxidermist who ship all over the US. Most have their own trailer to move full loads of mounts to keep costs down. If you know someone with an enclose trailer that has plywood walls you can attach a piece of strip of 1/2" plywood or 1x6" to the back and then screw that piece of plywood/wood/mount to the wall. That is how one taxidermist I used in Houston moved mounts all over the state and US.
^^^^^^^^^^^^^THIS^^^^^^^^^^^^^^
My cousin has a couple different guys that he uses to ship his mounts throughout the US and they do it exactly like stxranchman describes above.