While I am sorry I don't have much advice, your post did make me smile. The visual created in my mind after reading about your kitten "riding" the Littermaid much like an amusement park ride was too cute!
You can't limit access because afterall, it is the litterbox...so I can see where you would have a problem in correcting this. Do you think the box will cause her physical harm or injury if she continues? If so, then I might think about replacing the Littermaid with a box that she doesn't show so much interest in turning into entertainment.
As an amusing side note, I know of a cat (not mine) that LOVES the vacuum cleaner. Most cats I know are totally terrified of vacs, so this amuses me in no small amount. Timmytoes (the cat) runs TO the vac whenever he hears Diane getting it out, not away from it like my cats all do. It is a Hoover cannister-type and he jumps up on the cannister part and when Diane pulls it around the house he rides on it right along behind her. In fact, I wrote a short children's story in which Timmytoes was a "Cowboy" cat and the name of his trusty steed was Hoover. *grin*
Let me know how things go,