My preferred method is to emulate factory packaging and use a backcard!
Make a couple of holes around the feet, neck and/or back and tie with twist ties or string/ribbon. String or satin ribbon is probably better for fully painted customs but I've used twist ties, too. Put the backcard in a box and firmly attach it to one of the walls so that it won't move during transit. I would probably section off the box to prevent the other ponies from squishing the hair.
This method also works for sculpted customs - make sure there's air around the part you want to protect and that the pony won't move during transit. With sculpted customs the card is usually best placed under the pony's feet, unless the sculpting is mainly on one side.