I took a different direction with a carousel I implemented, opting for bxSlider instead of jCarousel. This is for an image gallery I am building http://rjwcollective.com/equ
As the website says: you have the slideshowContainer to be attached to a variable in order to use the public functions. As reloadShow() and destroyShow() are public functions, this is the only way to go. Worked perfectly for me.
I've simply put a
var $theslideshow = [functionThatCallsYourSlideshow]
before my function and called afterwards $theslideshow.destroyShow();
hope this helps