Get a good size box, put an ass load of bubble wrap and put fragile stickers all over. Make sure it’s on the top row. About all you can do unless you wanna make a custom wooden box that’ll cost you 50-100$ in material and another x amount of hours to build.
I moved a bunch of mounts 1500 miles from CO to BC in my cargo trailer and pickup canopy…multiple loads. Size ranged from pronghorn up to moose including elk and kudu. We used a pile of packing blankets, soft furniture, lots of cord and rope to stabilize them etc. Really did not have any issues. Just do not let antlers dig into capes etc. Some were upside down resting on the antler tops and top of shoulder, others on the back of the mount, etc.
About the only visible damage was a small spot an a 35 yr old mule deer mount with very brittle hair.
For a moving company to crate them would have cost $500 just for each mount box plus the cost of shipping was quoted extremely high due to extreme volume and weight. Not practical or cost effective for us.
Was really nice to get them up in our house build! But that took having scaffolding, etc. Not easy, not to mention paperwork at the border to bring them to Canada as part of our move up here.
Moving a single one I’ve just put it the back of the SUV with blankets, when I’ve moved lots of stuff and several months I’ve made crates out of 1/4” OSB sized appropriately for each mount. I had a hanging hook in the box and then ran a screw through the box into the back of the mount so it couldn’t fall off.
Move often. Buddy talked me on to how to build plywood crates. I can fit two smaller mounts in one about 24”x24”x 48” and it works pretty well. Weighs maybe 60lbs so easily moveable with handles. Cost me $80 a few years ago to build.
Survived three moves, some overseas.
Got a quote from my taxidermist recently for $300 to build one for my bull. Probably reasonable given wood is double in cost, this would be double in size (easy) and an hour of labor.