That fuji is a pretty looking bike.

As far as your shifting issues I would suspect the internal cable routing to be at fault. perhaps it is twisted around a second cable inside the frame or has a wierd kink in it somehow. do all of your cable housing ends have metal caps on them? is it brake cable housing or deraileur cable housing?

Until you resolve the issue I would get a chain catcher to prevent your chain from damaging the carbon of your bottom bracket. $20 on ebay mine is made by token.