Isn’t half off the seat clamp on the cx connected to the unicycle? And the only things that comes off is the seat clamp handle? At least that’s how it is on my old cx, maybe they upgraded it. I don’t think you could really buy any other seat clamp and have it fit without sawing down the frame. You may just be better off getting a large screw and bolt cover at the end so it doesn’t mess up her knees.
Mine on my Surly does the same thing, but it’s a screw clamp one anyways. I need to take it to my LBS and have them put a different one on. Only falls make it rotate though. So weird, it must be really close to the right size but oh so short when it knocks the seat in a fall.