Loxie,
My advice was going to be the same as Dan's, use a rasp, small triangle shaped file or just a utility knife and cut some grooves along the round parts just before the "corners" so the rush doesn't slip.
But what an odd chair, caned back and rush seat? That's just plane weird. Are you sure that's original and somebody didn't just change it because that's what they knew how to do?
Can you send me a picture before taking it apart so I can post it to the Forum PictureTrail Album?
The Wicker Woman®--Cathryn Peters
http://www.WickerWoman.com/seatweaving