2 options that both work...plus one good bonus option...
The ghost-shifting was a major problem especially with the 02 and 03 models. Giant finally recognized that this problem was being caused by the flexion of the seatstays, which in turn slackens the cable and allows the rd to shift. Giant redesigned their '04 frame with stiffer seatstays. I suffered with this problem with my '02 frame until I finally found the solution after nearly 2 years.
Option 1: GOOD - The cable slackens between the two cable stops on the seat stay. Remedy this by running one continuous piece of housing from the top tube (nearest the seat tube) down to the rear derailleur. This way, when the seatstay flexes it will not affect the cable itself. You can even Dremmel out the stops and run the housing through them to make it all cleaner. I've used this on a few NRS frames, and the customers report a lot less problems.
Option 2: PERMANENT END TO PROBLEM - switch to a setup that uses an SRAM rear derailleur. It's not hype - this really works. The Shimano derailleurs take very little cable movement to shift the rd, such as the small amount that you get from seatstay flex. SRAM derailleurs take more cable movement to actuate a shift, so even with seatstay flex and a little slackening in the cable, the derraileur will stay put. No ghost-shifting...guaranteed. Every frame that I've switched to SRAM has reported perfect shifting, with no chain skip or ghost shifting at all. Problem solved.
Option 3: This one is good - since you already have an 04 frame this may not help, but hopefully it will help others with older frames and the notorious ghost-shifting problem. Giant, having recognized the ghost shifting problems, will replace older frames with current 04 models.
If money is a factor, go with the rerouting of the cable. If you've got some cash to spare, switch to SRAM. If you can go a couple of weeks without your bike, call Giant and get a brand new 04 frame.