Thanks to everyone, and...

Success! I just tried your suggestion, dabac, and it worked like a charm. Well, she put up a fight, but gave up the ghost after a few firm twists. Thank you!

Look at all this rust:

http://img.photobucket.com/albums/v6.../iphone009.jpg
http://img.photobucket.com/albums/v6.../iphone010.jpg

Bonus question: I'm sure there's a lot of rust inside the head tube, any easy way of getting at that without damaging anything?