I have an Avonite top with a chip, 1/4" wide by 1/6" deep. I have the old
> sink cut out for repair material and bought a new tube of the original
> epoxy. Ideally, I am tiring to find a 3/8" tapered bit with a MATCHING
> 3/8" tapered plug cutter. Is there such a thing out there? Where can I
> procure one? If not, What is the best way to repair?

Did you try sanding the scratch out? Depending in the finish, try 250 for matte finish and 400 for satin finish. There is info on the Avonite web site.
All else fails, you'll have to call an installer for repairs.