Just checked on TISS.COM and found a 500 DM (less than $400 US) fare on UNITED from Frankfurt to Taipei. There was no seat availability on the 4th of Feb. but you might check other dates and find out from the consolidator more about that fare. You can easily get cheap flights to Frankfurt if you can figure out how to wangle this one. I don't know what the routing would be or how much you would be on United but at this rate and given your willingness to punish yourself for miles, give it a try! Don't be surprised if they are all sold out at this price.