How can I fit a tapered fork to a 1 1/8 semi-integrated/zero stack head tube? I have a 2004 Giant VT frame with a zero stack / semi-integrated headset.  It currently takes a straight steerer threadless fork.

Is there any type of headset I can put on so I can fit a tapered fork?
There are products like the Cane Creek 40.EC44/40.Bottom Assembly (Here's a press article on it and its kin, which should read first) which may work (I know its been installed successfully on some other Giant bikes, such as the Anthem, but not on your particular bike). Theres a lift of the front end by 5-10 mm, so its not a free lunch (aside from the cost of the unit and ancillaries). You should go to your LBS and test this actually works with this or a similar unit and the desired fork though, before you drop the money on it.