A quality rebuild kit would be my first stop. Probably a new float as well.
I have zero experience with that late a carburetor, so search here a bit, and wait for everybody to get back from Halloween parties. I'll bet Reed can help you out!
I'm not sure, but you may have an electronically controlled carburetor that needs specific techniques to correctly set up. Make sure your comfortable working on such a device before opening it up.
Remanufactured carburetors are a crap shoot. Most are junk, so don't turn your carburetor in for a core or throw it away. In many cases a good rebuilder can fix your carb more easily than something that's been messed up by a reman company. Holley makes the best remanufactured carbs that I've run across, but that's just my experience.
CJ