Hi Paul
I have had a slightly different problem being what seems to be a frequent problem with the BMW cars, spinning barrel. This also requires the barrel to be removed therefore the following should help you. A search of web sites came up with two good articals. I have added the links you may need to copy and paste them into your browser bar. Read both as the first does seem rather technical and maybe not necessary for the Z3 that may not have the bit broken that is referred to. The second is clear and there are photos also. Read all the thread.
Good luck. I am off to the scrap yard soon to try out the instructions before I have a go on the Z3.
http://www.unitedbimmer.com/forums/e36/13574-spinning-ignition-barrel-repair.html
http://forum.bmwcarmagazine.com/viewtopic.php?t=15445
Doug, May 2009