How can I ship a fragile, sentimental cactus plant across country?

You can use thick layers of newspaper and old carpeting. If this is a large, tall cactus, open a newspaper and wrap the full thickness around the cactus.Use as many newspapers as it will take to cover the cactus. Tie each layer with cord securely. Then wrap it with the carpet. Tie this securely. Make sure the cactus is secured so that it cannot fall. Make sure the pot is secured to the floor so that sudden stops won't have the pot sliding away while the cactus stays tied up, breaking the cactus off.