A Fun Javascript Puzzle: Shortcut Icons

Someone at work asked about this and I can’t find the answer. And, because my foot hurts and I can’t sleep, I figured I’d give it a shot.
This is my attempt, and it doesn’t work in anything but Opera 8.5 (that I’ve tested so far), as you can see. Any ideas?
Before you start, here’s what I found with my example:
# Firefox and Safari both report no errors when I try to change the shortcut icon.
# Firefox actually updates the DOM to point to the new image, but the browser doesn’t display it.
# It doesn’t work in IE, but I had someone else test it and I didn’t get any more details other than it doesn’t work.
# I’ve only tried one way of doing it so far, but I can’t think of anything else that would work at the moment (paaaaaain piiiiiiiills).
Got any ideas? Isn’t it a fun little conundrum?
UPDATE: I’ve got something working in Firefox! Check out attempt two. It removes the shortcut icon link and appends a new one to the head. Still doesn’t work in Safari, and I don’t have IE at the moment to test, but it’s progress. If you try it in IE, please let me know if it works.