Perhaps you could stuff clothes into them? This would make them "solid" and less likely to bend. You could roll little tee shirts and shorts, then fill the void of the crown with the little rolls (or socks and underwear.) Around the outside of the crowns you could do the same thing. Don't overpack the case, so they don't crush as you squeeze it closed - and hardside luggage will be less likely to bruise them.
I'll be interested in what other people suggest....
Maddle